Kenali konsep dan cara memperoleh nilai suku banyak (polinomial) dengan membaca penjelasan di artikel Matematika kelas 11 berikut ini! Ada contoh soalnya juga lho, jangan sampai kelewatan!
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Matematika itu bisa dibilang berperan penting untuk kehidupan kita. Kegiatan yang biasanya kita lakukan pasti ada hubungannya dengan matematika.
Misalnya, jajan, masak, olahraga, bermain, duhh banyak banget, deh! Bahkan, tanpa sadar, kita menggunakan matematika untuk membantu pekerjaan kita, loh!
Contohnya, ketika kamu ingin membuat suatu prakarya berbentuk kubus dengan volume tertentu yang terbuat dari kardus, kamu butuh kalkulasi yang akurat. Kamu perlu menentukan panjang, lebar, tinggi kardus, dan juga ukuran sisi lipatannya. Nah, untuk menentukan hal itu, kamu bisa menggunakan matematika, salah satunya dengan aturan suku banyak.
“Hah?! Suku banyak? Apaan, tuh?”
Yuk, baca sampai habis, ya!
Pengertian Suku Banyak
Suku banyak adalah suatu bentuk matematika yang merupakan penjumlahan atau pengurangan dari satu suku atau lebih dengan pangkat variabelnya harus bilangan bulat dan tidak negatif. Suku banyak disebut juga polinomial. Bentuk umumnya seperti ini, nih!
Bentuk umum suku banyak (polinomial).
Coba perhatikan bentuk umumnya, anxn ,an-1xn-1, dan seterusnya disebut suku. Jadi, suku itu terdiri dari variabel beserta koefisiennya atau konstanta.
Nah, dari bentuk umum kelihatan ya, urutan suku banyak itu dimulai dari suku dengan pangkat tertinggi (anxn), lalu diikuti oleh suku-suku dengan pangkat yang semakin menurun (an-1xn-1, an-2xn-2,…, a2x2, a1x1), dan diakhiri oleh suku dengan pangkat nol (a0).
Baca Juga: Memahami Konsep Turunan Fungsi Aljabar
Pangkat tertinggi variabel pada suku banyak ini disebut dengan derajat. Kalau dari bentuk umum di atas, derajatnya adalah n ya, karena n adalah pangkat tertinggi variabel dari bentuk umum suku banyak ini.
Oh iya, suku banyak itu variabelnya nggak harus satu ya, tapi bisa juga memiliki lebih dari satu variabel. Selain itu, variabel suku banyak nggak mesti dalam huruf x aja, tapi bisa dalam huruf y atau huruf-huruf yang lain.
Gimana? Paham ya bentuk suku banyak itu seperti apa?
Nah, kalau kamu lihat contoh suku banyak di atas, setiap sukunya akan digabungkan oleh operasi penjumlahan atau pengurangan, ya. Oh iya, ada beberapa hal yang harus kamu perhatikan juga, nih!
- Pastikan variabel berada sebagai pembilang dengan pangkat variabelnya harus bilangan bulat dan tidak negatif.
- Bukan merupakan suku yang tak terbatas.
Kamu tahu, nggak? Penerapan suku banyak ternyata banyak banget lho dalam kehidupan kita. Yaaa… Selain bisa digunakan untuk mengukur struktur bangunan tertentu, seperti pada contoh kasus di awal artikel ini, suku banyak juga bisa digunakan untuk menghitung banyak barang, menyajikan pola cuaca di daerah tertentu, dan masih banyak lagi. Kita juga bisa menuliskan kalimat atau pernyataan secara lebih ringkas dan efisien menggunakan suku banyak.
Baca Juga: Cara Mencari Determinan dan Invers Matriks
Nah, sudah lebih paham kan sekarang tentang suku banyak atau polinomial? Next, langsung aja yuk kita bahas cara memperoleh nilai suku banyak.
Suku banyak atau polinomial merupakan bentuk aljabar yang memuat suatu variabel. Oleh karena itu, suku banyak bisa kita tulis dalam bentuk fungsi dari variabelnya. Misalnya, suku banyak dengan variabel x dapat kita tulis sebagai fungsi dari x (f(x)).
Selain f(x), fungsi suku banyak juga bisa dinyatakan dengan S(x) yang menyatakan fungsi suku banyak dengan variabel x, atau P(x) yang menunjukkan fungsi polinom suku banyak dalam variabel x.
Cara Mencari Nilai Suku Banyak
Nah, cara mencari nilai suku banyak bisa dilakukan dengan cara substitusi atau cara Horner.
1. Cara Substitusi
Untuk cara ini, pasti kamu sudah mengerti, kan? Itu loh, mengganti variabel x dengan suatu bilangan yang diketahui. Contohnya:
1. Tentukan nilai suku banyak untuk x = 3, jika diketahui f(x) = 4x3 – 2x2 + 9.
Pembahasan:
f(x) = 4x3 – 2x2 + 9 (substitusikan nilai 3 ke setiap x-nya)
f(3) = 4(3)3 – 2(3)2 + 9
f(3) = 4(27) – 18 + 9
f(3) = 108 – 9 = 99
Jadi, nilai suku banyak f(x) = 4x3 – 2x2 + 9 untuk x = 3 adalah 99.
2. Tentukan nilai suku banyak 7x3 + 6x2 – 5x + 20 untuk x = -1
Pembahasan:
f(x) = 7x3 + 6x2 – 5x + 20 (substitusikan nilai -1 ke setiap x-nya)
f(-1) = 7(-1)3 + 6(-1)2 – 5(-1) + 20
f(-1) = -7 + 6 + 5 + 20 = 24
Jadi, nilai suku banyak f(x) = 7x3 + 6x2 – 5x + 20 untuk x = -1 adalah 24.
Wah, cukup mudah, kan? Tapi, sewaktu kamu mengoperasikan bilangannya, harus teliti, ya!
Baca Juga: Konsep Limit Fungsi Aljabar dan Sifat-Sifatnya
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Istirahat dulu, yuk! Sambil istirahat, kakak mau kasih kamu info nih, kalau di ruangbelajar, sekarang ada fitur bernama Adapto. Adapto ini bisa menyesuaikan video dengan kemampuan belajarmu, lho! Penasaran, kan? Jangan lupa, cobain ya!
2. Cara Horner
Nah, sebelum masuk ke penjelasannya, kita lihat dulu yuk matematikawan yang berperan penuh pada metode atau cara horner ini!
Oke, untuk mendapatkan nilai suku banyak dengan cara horner, ada beberapa langkah yang harus kamu lakukan, nih. Eits! Langkah-langkahnya nggak sulit, kok! Perhatikan baik-baik, ya.
Misalnya mencari nilai suku banyak P(x) = ax3 + bx2 + cx + d saat x = k.
Step 1: Tuliskan setiap koefisien pada fungsi suku banyak secara terurut. Dimulai dari koefisien suku dengan pangkat tertinggi sampai terendah.
Jika salah satu suku dari pangkat terurut tidak ada, maka tuliskan dengan angka nol. Contohnya, P(x) = ax3 + cx + d. Fungsi suku banyak tersebut terdiri dari variabel dengan pangkat 3, 1, dan 0 (tidak ada pangkat 2). Jadi, untuk penulisannya, koefisien suku dengan pangkat 2 tetap kita tulis, namun diisi dengan angka nol.
Step 2: Tuliskan nilai x = k yang telah diketahui, di sisi paling kiri.
Step 3: Isi daerah hasil (baris ke-3) kolom pertama dengan koefisien awal.
Step 4: Kalikan hasil dari step 3 dengan k, lalu letakkan hasilnya di baris kedua kolom dua.
Step 5: Jumlahkan koefisien kedua yang ada pada baris pertama dengan baris kedua, lalu letakkan hasilnya pada baris ketiga.
Ulangi step tersebut sampai diperoleh hasil akhir.
Jadi nilai suku banyak P(x) = ax3 + bx2 + cx + d saat x = k adalah ak3 + bk2 + ck + d.
Baca Juga: Kedudukan Titik dan Garis Lurus terhadap Lingkaran
Nah, supaya lebih jelas, langsung ke contoh soal aja, yuk!
Contoh Soal Polinomial
1. Hitunglah nilai suku banyak dari g(x) = 3x3 + x2 + 2x – 5, untuk x = 4!
Pembahasan:
Step 1: Tulis setiap koefisien suku banyak pada baris ke-1. Ditulis berurut ya, dimulai dari koefisien suku dengan pangkat tertinggi, yaitu 3 sampai koefisien suku dengan pangkat terendah, yaitu -5.
Step 2: Tulis nilai x = 4 di sisi paling kiri, diikuti dengan menulis koefisien suku pertama, yaitu 3 di baris ke-3 atau daerah hasil.
Step 3: Kalikan 4 dengan hasil dari step 2, yaitu 3. Lalu, letakkan hasilnya, yaitu 12 di kolom ke-2 baris ke-2.
Step 4: Jumlahkan angka 1 (koefisien suku ke-2) dengan 12 (hasil dari step 3), sehingga diperoleh hasil 13. Kemudian, kalikan kembali 4 dengan 13. Jangan lupa hasilnya, yaitu 52 diletakkan pada baris ke-2 kolom ke-3.
Step 5: Mirip cara sebelumnya, kita jumlahkan koefisien suku ke-3, yaitu 2 dengan 52 dan hasilnya letakkan di baris ke-3 kolom ke-3.
Step 6: Terakhir, kalikan kembali 4 dengan 54, hasilnya 216 diletakkan di baris ke-2 kolom ke-4. Kemudian, -5 sebagai suku terakhir dijumlahkan dengan 216, dan diperoleh hasil 211.
Jadi, nilai suku banyak g(x) = 3x3 + x2 + 2x – 5 untuk x = 4 adalah 211.
Menurut kamu, lebih mudah cara horner apa substitusi, nih?
Nah, kalau dalam satu soal kamu menggunakan dua cara itu dan didapat hasil yang berbeda, itu berarti, ada yang salah tuh waktu mengoperasikannya. Coba deh kamu periksa kembali.
Sekarang, aku mau challenge kamu untuk menyelesaikan 2 soal dibawah ini dan tulis jawabannya di kolom komentar yaa, good luck!
Wah, seru banget kan materi suku banyak ini? Tapi, sebenarnya masih banyak loh materi suku banyak (polinomial) yang bisa kamu gali. Ada teorema sisa, teorema faktor, akar-akar suku banyak, dan operasi suku banyak. Kita akan bahas di next artikel, ya! Pokoknya seru-seru banget deh untuk dipelajari!
Nah, setelah baca artikel ini, supaya konsepnya lebih mantap, langsung aja yukk latihan soal di ruangbelajar. Tenang guys, latihan soalnya udah lengkap dengan pembahasannya kok, dan yang lebih kerennya lagi, ada fitur ruangguru live. Jadi, kamu bisa ikut belajar secara langsung. Asik banget, kan? selamat belajar, yaaa!
Referensi:
Wirodikromo, S. (2007). Matematika Jilid 2 IPA untuk kelas XI. Jakarta: Erlangga.
‘Penerapan Polinomial dalam Pengembangan Ilmu dan Teknologi Sehari-hari’, Kemendikbud. [Daring]. Tautan: https://sumberbelajar.seamolec.org/product.php?id=NWFjYzU3MDQ4NjVlYWM2YzA1MzIxY2Ez (Diakses 17 Oktober 2020)
‘William George Horner’, Britannica. [Daring]. Tautan: https://www.britannica.com/biography/William-George-Horner (Diakses 17 Oktober 2020)
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<h1 class="content-title">
Mempelajari Konsep dan Nilai Suku Banyak (Polinomial) | Matematika Kelas 11 </h1>
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<p class="content-author"><a href="https://www.ruangguru.com/blog/author/kak-efira-mt-saintek" class="">Kak Efira MT Saintek</a> </p>
<p class="content-info"><span>October 15, 2025 • </span> <span>7 minutes read</span></p>
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<p><em><img decoding="async" style="width: 820px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Mempelajari%20Konsep%20dan%20Nilai%20Suku%20Banyak.jpg" alt="Mempelajari Konsep dan Nilai Suku Banyak" /></em></p>
<blockquote>
<p style="text-align: center;"><em>Kenali konsep dan cara memperoleh nilai suku banyak (polinomial) dengan membaca penjelasan di <strong><a href="https://www.ruangguru.com/blog/c/matematika/matematika-sma-kelas-11">artikel Matematika kelas 11</a></strong> berikut ini! Ada contoh soalnya juga lho, jangan sampai kelewatan!</em></p>
<p style="text-align: center;"><em>—</em></p>
</blockquote>
<p> </p>
<p style="text-align: justify;"><a href="/blog/logika-matematika" rel="noopener"><strong>Matematika itu</strong></a> bisa dibilang berperan penting untuk kehidupan kita. Kegiatan yang biasanya kita lakukan pasti ada hubungannya dengan matematika.</p>
<p style="text-align: justify;">Misalnya, jajan, masak, olahraga, bermain, duhh banyak banget, deh! Bahkan, tanpa sadar, kita menggunakan matematika untuk membantu pekerjaan kita, loh!</p>
<p style="text-align: justify;">Contohnya, ketika kamu ingin membuat suatu prakarya berbentuk kubus dengan volume tertentu yang terbuat dari kardus, kamu butuh kalkulasi yang akurat. Kamu perlu menentukan panjang, lebar, tinggi kardus, dan juga ukuran sisi lipatannya. Nah, untuk menentukan hal itu, kamu bisa menggunakan matematika, salah satunya dengan aturan <strong><a href="/blog/operasi-suku-banyak-dan-konsep-sisa" rel="noopener">suku banyak</a></strong>.</p>
<p style="text-align: justify;">“Hah?! Suku banyak? Apaan, tuh?”</p>
<p style="text-align: justify;"> Yuk, baca sampai habis, ya!</p>
<p> </p>
<h2><span style="font-size: 18pt;">Pengertian Suku Banyak</span></h2>
<p style="text-align: justify;"><strong>Suku banyak adalah suatu bentuk matematika yang merupakan penjumlahan atau pengurangan dari satu suku atau lebih dengan pangkat variabelnya harus bilangan bulat dan tidak negatif</strong>. Suku banyak disebut juga polinomial. Bentuk umumnya seperti ini, nih!</p>
<p><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Bentuk%20Umum%20Suku%20Banyak%20Polinomial.jpg" alt="Bentuk Umum Suku Banyak Polinomial" /></p>
<p style="text-align: center;">Bentuk umum suku banyak (polinomial).</p>
<p> </p>
<p>Coba perhatikan bentuk umumnya,<span style="color: #000000;"> a<sub>n</sub>x<sup>n</sup> ,a<sub>n-1</sub>x<sup>n-1</sup>, </span>dan seterusnya disebut suku. Jadi, suku itu terdiri dari variabel beserta koefisiennya atau konstanta.</p>
<p style="text-align: justify;">Nah, dari bentuk umum kelihatan ya, urutan suku banyak itu dimulai dari suku dengan pangkat tertinggi<span style="color: #000000;"> (a<sub>n</sub>x<sup>n</sup>), </span>lalu diikuti oleh suku-suku dengan pangkat yang semakin menurun<span style="color: #000000;"> (a<sub>n-1</sub>x<sup>n-1</sup>, a<sub>n-2</sub>x<sup>n-2</sup>,…, a<sub>2</sub>x<sup>2</sup>, a<sub>1</sub>x<sup>1</sup>), </span>dan diakhiri oleh suku dengan pangkat nol<span style="color: #000000;"> (a<sub>0</sub>). </span></p>
<p><strong>Baca Juga: <a href="/blog/turunan-fungsi-aljabar" rel="noopener">Memahami Konsep Turunan Fungsi Aljabar</a></strong></p>
<p style="text-align: justify;"><strong>Pangkat tertinggi variabel pada suku banyak ini disebut dengan</strong> <strong>derajat</strong>. Kalau dari bentuk umum di atas, derajatnya adalah <strong>n</strong> ya, karena n adalah pangkat tertinggi variabel dari bentuk umum suku banyak ini.</p>
<p style="text-align: justify;">Oh iya, suku banyak itu variabelnya nggak harus satu ya, tapi bisa juga memiliki lebih dari satu variabel. Selain itu, variabel suku banyak nggak mesti dalam huruf x aja, tapi bisa dalam huruf y atau huruf-huruf yang lain.</p>
<p><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Contoh%20Suku%20Banyak%20Polinomial.jpg" alt="Contoh Suku Banyak Polinomial" /></p>
<p> </p>
<p style="text-align: justify;">Gimana? Paham ya bentuk suku banyak itu seperti apa?</p>
<p style="text-align: justify;">Nah, kalau kamu lihat contoh suku banyak di atas, setiap sukunya akan digabungkan oleh operasi penjumlahan atau pengurangan, ya. Oh iya, ada beberapa hal yang harus kamu perhatikan juga, nih!</p>
<ol>
<li style="text-align: justify;">Pastikan variabel berada sebagai pembilang dengan pangkat variabelnya harus bilangan bulat dan tidak negatif.</li>
<li style="text-align: justify;">Bukan merupakan suku yang tak terbatas.</li>
</ol>
<p> </p>
<p><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Contoh%20Bukan%20Suku%20Banyak%20Polinomial.jpg" alt="Contoh Bukan Suku Banyak Polinomial" /></p>
<p> </p>
<p style="text-align: justify;">Kamu tahu, nggak? <strong>Penerapan suku banyak</strong> ternyata banyak banget lho dalam kehidupan kita. Yaaa… Selain bisa digunakan untuk mengukur struktur bangunan tertentu, seperti pada contoh kasus di awal artikel ini, suku banyak juga bisa digunakan untuk menghitung banyak barang, menyajikan pola cuaca di daerah tertentu, dan masih banyak lagi. Kita juga bisa menuliskan kalimat atau pernyataan secara lebih ringkas dan efisien menggunakan suku banyak.</p>
<p style="text-align: justify;"><strong>Baca Juga: <a href="/blog/cara-mencari-determinan-dan-invers-matriks" rel="noopener">Cara Mencari Determinan dan Invers Matriks</a></strong></p>
<p style="text-align: justify;">Nah, sudah lebih paham kan sekarang tentang suku banyak atau polinomial? Next, langsung aja yuk kita bahas cara memperoleh nilai suku banyak.</p>
<p> </p>
<h2><span style="font-size: 18pt;">Nilai Suku Banyak</span></h2>
<p style="text-align: justify;">Suku banyak atau polinomial merupakan bentuk aljabar yang memuat suatu variabel. Oleh karena itu, suku banyak bisa kita tulis dalam bentuk fungsi dari variabelnya. Misalnya, suku banyak dengan variabel x dapat kita tulis sebagai fungsi dari x (f(x)).</p>
<p><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Fungsi%20Suku%20Banyak%20Polinomial.jpg" alt="Fungsi Suku Banyak Polinomial" /></p>
<p> </p>
<p style="text-align: justify;">Selain f(x), fungsi suku banyak juga bisa dinyatakan dengan S(x) yang menyatakan fungsi suku banyak dengan variabel x, atau P(x) yang menunjukkan fungsi polinom suku banyak dalam variabel x.</p>
<p> </p>
<h2><span style="font-size: 18pt;">Cara Mencari Nilai Suku Banyak</span></h2>
<p style="text-align: justify; font-weight: normal;">Nah, cara mencari nilai suku banyak bisa dilakukan dengan <strong>cara substitusi atau cara Horner</strong>.</p>
<p> </p>
<h3><span style="font-size: 14pt;">1. Cara Substitusi</span></h3>
<p style="text-align: justify;">Untuk cara ini, pasti kamu sudah mengerti, kan? Itu loh, mengganti variabel x dengan suatu bilangan yang diketahui. Contohnya:</p>
<p style="text-align: justify; font-size: 16px;"><span style="color: #000000;">1. <span style="background-color: transparent;">Tentukan nilai suku banyak untuk x = 3, jika diketahui f(x) = 4x<sup>3 </sup>– 2x<sup>2 </sup>+ 9.</span></span></p>
<p style="text-align: justify; font-size: 16px;"><span style="color: #000000;"><strong>Pembahasan:</strong></span></p>
<p style="text-align: justify; font-size: 16px;"><span style="color: #000000;">f(x) = <span style="background-color: transparent;">4x<sup>3 </sup>– 2x<sup>2 </sup>+ 9 (substitusikan nilai 3 ke setiap x-nya)</span></span></p>
<p style="text-align: justify; font-size: 16px;"><span style="color: #000000;">f(3) = <span style="background-color: transparent;">4(3)<sup>3 </sup>– 2(3)<sup>2 </sup>+ 9</span></span></p>
<p style="text-align: justify; font-size: 16px;"><span style="color: #000000;">f(3) = 4(27) – 18 + 9</span></p>
<p style="text-align: justify; font-size: 16px;"><span style="color: #000000;">f(3) = 108 – 9 = 99</span></p>
<p style="text-align: justify; font-size: 16px;"><span style="color: #000000;">Jadi, nilai suku banyak f(x) = <span style="background-color: transparent;">4x<sup>3 </sup>– 2x<sup>2 </sup>+ 9</span> untuk x = 3 adalah 99.</span></p>
<p> </p>
<p><span style="color: #000000;">2. Tentukan nilai suku banyak 7x<sup>3 </sup>+ 6x<sup>2 </sup>– 5x + 20 untuk x = -1</span></p>
<p><span style="color: #000000;"><strong><span style="background-color: transparent;">Pembahasan:</span></strong></span></p>
<p><span style="color: #000000;">f(x) = 7x<sup>3 </sup>+ 6x<sup>2 </sup>– 5x + 20 (substitusikan nilai -1 ke setiap x-nya)</span></p>
<p><span style="color: #000000;">f(-1) = 7(-1)<sup>3 </sup>+ 6(-1)<sup>2 </sup>– 5(-1) + 20 </span></p>
<p><span style="color: #000000;">f(-1) = -7 + 6 + 5 + 20 = 24</span></p>
<p><span style="color: #000000;">Jadi, nilai suku banyak f(x) = 7x<sup>3 </sup>+ 6x<sup>2 </sup>– 5x + 20 untuk x = -1 adalah 24.</span></p>
<p style="text-align: justify;"><span style="color: #000000;"><em>Wah</em>, cukup mudah, <em>kan</em>? Tapi, sewaktu kamu mengoperasikan bilangannya, harus teliti, ya!</span></p>
<p><strong>Baca Juga: <a href="/blog/konsep-limit-fungsi-aljabar-dan-sifat-sifatnya" rel="noopener">Konsep Limit Fungsi Aljabar dan Sifat-Sifatnya</a></strong></p>
<p style="text-align: center;">—</p>
<blockquote>
<p style="text-align: center;"><em>Istirahat dulu, yuk! Sambil istirahat, kakak mau kasih kamu info nih, kalau di ruangbelajar, sekarang ada fitur bernama Adapto. Adapto ini bisa menyesuaikan video dengan kemampuan belajarmu, lho! Penasaran, kan? Jangan lupa, cobain ya!</em></p>
</blockquote>
<p style="text-align: justify;"><span style="color: #000000;"><span style="font-weight: normal;"><a class="rg-cta" style="text-align: center;" href="https://www.ruangguru.com/ruangbelajar" target="_blank" rel="noopener"><img decoding="async" class="aligncenter" src="https://cdn-web.ruangguru.com/landing-pages/assets/cta/5a2e155b-2bf0-40bf-8b0a-a0a498e7732d.jpeg" alt="IDN CTA Blog Adapto Ruangguru 2022" width="820" /></a></span></span></p>
<p> </p>
<h3><span style="font-size: 14pt;">2. Cara Horner</span></h3>
<p style="text-align: justify;">Nah, sebelum masuk ke penjelasannya, kita lihat dulu yuk matematikawan yang berperan penuh pada metode atau cara horner ini!</p>
<p style="font-size: 16px;"><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/William%20G%20Horner.jpg" alt="William G Horner" /></p>
<p> </p>
<p style="text-align: justify;">Oke, untuk mendapatkan nilai suku banyak dengan cara horner, ada beberapa langkah yang harus kamu lakukan, nih. Eits! Langkah-langkahnya nggak sulit, kok! Perhatikan baik-baik, ya.</p>
<p style="text-align: justify;"><span style="color: #000000;">Misalnya mencari nilai suku banyak P(x) = ax<sup>3</sup> + bx<sup>2</sup> + cx + d saat x = k.</span></p>
<p style="font-size: 16px; text-align: justify;"><span style="color: #000000;"><strong>Step 1:</strong> Tuliskan setiap koefisien pada fungsi suku banyak secara terurut. Dimulai dari koefisien suku dengan pangkat tertinggi sampai terendah.</span></p>
<p style="font-size: 16px; text-align: justify;"><img decoding="async" style="width: 600px; display: block; margin: 0px auto;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/cara%20horner%201.jpg" alt="cara horner 1" /></p>
<p style="font-size: 16px; text-align: justify;"><span style="color: #000000;">Jika salah satu suku dari pangkat terurut tidak ada, maka tuliskan dengan angka nol. Contohnya, P(x) = ax<sup>3 </sup>+ cx + d. Fungsi suku banyak tersebut terdiri dari variabel dengan pangkat 3, 1, dan 0 (tidak ada pangkat 2). Jadi, untuk penulisannya, koefisien suku dengan pangkat 2 tetap kita tulis, namun diisi dengan angka nol.</span></p>
<p style="font-size: 16px;"><img decoding="async" style="width: 600px; display: block; margin: 0px auto;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/cara%20horner%202.jpg" alt="cara horner 2" /></p>
<p style="font-size: 16px;"><span style="color: #000000;"><strong>Step 2:</strong> Tuliskan nilai x = k yang telah diketahui, di sisi paling kiri.</span></p>
<p style="font-size: 16px;"><img decoding="async" style="width: 600px; display: block; margin: 0px auto;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/cara%20horner%203.jpg" alt="cara horner 3" /></p>
<p style="font-size: 16px;"><span style="color: #000000;"><strong>Step 3:</strong> Isi daerah hasil (baris ke-3) kolom pertama dengan koefisien awal.</span></p>
<p style="font-size: 16px; text-align: justify;"><img decoding="async" style="width: 600px; display: block; margin: 0px auto;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/cara%20horner%204.jpg" alt="cara horner 4" /></p>
<p style="font-size: 16px; text-align: justify;"><span style="color: #000000;"><strong>Step 4:</strong> Kalikan hasil dari step 3 dengan k, lalu letakkan hasilnya di baris kedua kolom dua.</span></p>
<p style="font-size: 16px;"><img decoding="async" style="width: 600px; display: block; margin: 0px auto;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/cara%20horner%205.jpg" alt="cara horner " /></p>
<p style="text-align: justify;"><span style="color: #000000;"><strong>Step 5:</strong> Jumlahkan koefisien kedua yang ada pada baris pertama dengan baris kedua, lalu letakkan hasilnya pada baris ketiga.</span></p>
<p><img decoding="async" style="width: 600px; display: block; margin: 0px auto;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/cara%20horner%206.jpg" alt="cara horner 6" /></p>
<p><span style="color: #000000;">Ulangi step tersebut sampai diperoleh hasil akhir.</span></p>
<p><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Contoh%20Penyelesaian%20Horner.jpg" alt="Contoh Penyelesaian Horner" /></p>
<p><span style="color: #000000;">Jadi nilai suku banyak P(x) = ax<sup>3</sup> + bx<sup>2</sup> + cx + d saat x = k adalah ak<sup>3</sup> + bk<sup>2</sup> + ck + d.</span></p>
<p><strong>Baca Juga: <a href="/blog/kedudukan-titik-dan-garis-lurus-terhadap-lingkaran" rel="noopener">Kedudukan Titik dan Garis Lurus terhadap Lingkaran</a></strong></p>
<p><span style="color: #000000;"><em>Nah</em>, supaya lebih jelas, langsung ke contoh soal <em>aja</em>, <em>yuk</em>!</span></p>
<p> </p>
<h2><span style="font-size: 18pt;">Contoh Soal Polinomial</span></h2>
<p><span style="color: #000000;">1. Hitunglah nilai suku banyak dari g(x) = 3x<sup>3</sup> + x<sup>2</sup> + 2x – 5, untuk x = 4!</span></p>
<p><span style="color: #000000;"><strong>Pembahasan: </strong></span></p>
<p style="text-align: justify;"><span style="color: #000000;"><strong>Step 1: </strong>Tulis setiap koefisien suku banyak pada baris ke-1. Ditulis berurut ya, dimulai dari koefisien suku dengan pangkat tertinggi, yaitu 3 sampai koefisien suku dengan pangkat terendah, yaitu -5.</span></p>
<p style="text-align: justify;"><img decoding="async" style="width: 600px; display: block; margin: 0px auto;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/cara%20horner%208.jpg" alt="cara horner 8" /></p>
<p style="text-align: justify;"><span style="color: #000000;"><strong>Step 2:</strong> Tulis nilai x = 4 di sisi paling kiri, diikuti dengan menulis koefisien suku pertama, yaitu 3 di baris ke-3 atau daerah hasil.</span></p>
<p style="text-align: justify;"><img decoding="async" style="width: 600px; display: block; margin: 0px auto;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/cara%20horner%209.jpg" alt="cara horner 9" /></p>
<p style="text-align: justify;"><span style="color: #000000;"><strong>Step 3:</strong> Kalikan 4 dengan hasil dari step 2, yaitu 3. Lalu, letakkan hasilnya, yaitu 12 di kolom ke-2 baris ke-2.</span></p>
<p style="text-align: justify;"><img decoding="async" style="width: 600px; display: block; margin: 0px auto;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/cara%20horner%2010.jpg" alt="cara horner 10" /></p>
<p style="text-align: justify;"><span style="color: #000000;"><strong>Step 4:</strong> Jumlahkan angka 1 (koefisien suku ke-2) dengan 12 (hasil dari step 3), sehingga diperoleh hasil 13. Kemudian, kalikan kembali 4 dengan 13. Jangan lupa hasilnya, yaitu 52 diletakkan pada baris ke-2 kolom ke-3.</span></p>
<p style="text-align: justify;"><img decoding="async" style="width: 600px; display: block; margin: 0px auto;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/cara%20horner%2011.jpg" alt="cara horner 11" /></p>
<p style="text-align: justify;"><span style="color: #000000;"><strong>Step 5:</strong> Mirip cara sebelumnya, kita jumlahkan koefisien suku ke-3, yaitu 2 dengan 52 dan hasilnya letakkan di baris ke-3 kolom ke-3.</span></p>
<p><img decoding="async" style="width: 600px; display: block; margin: 0px auto;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/cara%20horner%2012.jpg" alt="cara horner 12" /></p>
<p style="text-align: justify;"><span style="color: #000000;"><strong>Step 6:</strong> Terakhir, kalikan kembali 4 dengan 54, hasilnya 216 diletakkan di baris ke-2 kolom ke-4. Kemudian, -5 sebagai suku terakhir dijumlahkan dengan 216, dan diperoleh hasil 211.</span></p>
<p><img decoding="async" style="width: 600px; display: block; margin: 0px auto;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/cara%20horner%2013.jpg" alt="cara horner 13" /></p>
<p><span style="color: #000000;">Jadi, nilai suku banyak g(x) = 3x<sup>3</sup> + x<sup>2</sup> + 2x – 5 untuk x = 4 adalah 211. </span></p>
<p style="text-align: justify;"><span style="color: #000000;">Menurut kamu, lebih mudah cara horner apa substitusi, <em>nih</em>?</span></p>
<p style="text-align: justify;"><span style="color: #000000;"><em>Nah</em>, kalau dalam satu soal kamu menggunakan dua cara itu dan didapat hasil yang berbeda, itu berarti, ada yang salah tuh waktu mengoperasikannya. Coba <em>deh</em> kamu periksa kembali.</span></p>
<p style="text-align: justify;"><span style="color: #000000;">Sekarang, aku mau <em>challenge</em> kamu untuk menyelesaikan 2 soal dibawah ini dan tulis jawabannya di kolom komentar yaa,<em> good luck!</em></span></p>
<p><em><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Latihan%20Soal%20Suku%20Banyak%20Polinomial.jpg" alt="Latihan Soal Suku Banyak Polinomial" /></em></p>
<p> </p>
<p style="text-align: justify;">Wah, seru banget kan <strong>materi suku banyak</strong> ini? Tapi, sebenarnya masih banyak loh materi <strong>suku banyak (polinomial)</strong> yang bisa kamu gali. Ada teorema sisa, teorema faktor, akar-akar suku banyak, dan operasi suku banyak. Kita akan bahas di next artikel, ya! Pokoknya seru-seru banget deh untuk dipelajari!</p>
<p style="text-align: justify;">Nah, setelah baca artikel ini, supaya konsepnya lebih mantap, langsung aja yukk latihan soal di <strong><a href="https://www.ruangguru.com/ruangbelajar" target="_blank" rel="noopener">ruangbelajar</a></strong>. Tenang guys, latihan soalnya udah lengkap dengan pembahasannya kok, dan yang lebih kerennya lagi, ada fitur ruangguru live. Jadi, kamu bisa ikut belajar secara langsung. Asik banget, kan? selamat belajar, yaaa!</p>
<p><a href="https://bayar.ruangguru.com/"><img decoding="async" class="aligncenter size-medium" src="https://cdn-web-2.ruangguru.com/landing-pages/assets/e3260f88-1749-4d3b-8973-be3aae07a94c.jpg" alt="CTA Ruangguru" /></a></p>
<p><strong>Referensi:</strong></p>
<p>Wirodikromo, S. (2007). Matematika Jilid 2 IPA untuk kelas XI. Jakarta: Erlangga.</p>
<p>‘Penerapan Polinomial dalam Pengembangan Ilmu dan Teknologi Sehari-hari’, Kemendikbud. [Daring]. Tautan: https://sumberbelajar.seamolec.org/product.php?id=NWFjYzU3MDQ4NjVlYWM2YzA1MzIxY2Ez (Diakses 17 Oktober 2020)</p>
<p>‘William George Horner’, Britannica. [Daring]. Tautan: https://www.britannica.com/biography/William-George-Horner (Diakses 17 Oktober 2020)</p>
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<img src="https://cdn-web-2.ruangguru.com/static/youtube.png" loading=" lazy" alt="Logo Youtube Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.linkedin.com/company/ruangguru-com">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/linkedin.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/linkedin.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/linkedin.png" loading=" lazy" alt="Logo LinkedIn Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.tiktok.com/@ruangguru">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/tiktok.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/tiktok.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/tiktok.png" loading=" lazy" alt="Logo TikTok Footer" width="32px" height="32px" />
</picture>
</a>
</nav>
</div>
<div class="col-lg-9">
<div class="row">
<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title">Produk Ruangguru</p>
<ul type="none">
<li><a href="https://roboguru.ruangguru.com" target="_blank">Roboguru</a></li>
<li><a href="https://www.ruangguru.com/roboguruplus">Roboguru Plus</a></li>
<li><a href="https://www.ruangguru.com/dafa-lulu">Dafa dan Lulu</a></li>
<li><a href="https://www.ruangguru.com/for-kids/kursus">Kursus for Kids</a></li>
<li><a href="https://www.ruangguru.com/for-kids">Ruangguru for Kids</a></li>
<li><a href="https://www.ruangguru.com/bisnis">Ruangguru for Business</a></li>
<li><a href="https://www.ruangguru.com/ruanguji">Ruanguji</a></li>
<li><a href="https://www.ruangguru.com/blog">Ruangbaca</a></li>
<li><a href="https://www.ruangguru.com/ruangkelas">Ruangkelas</a></li>
<li><a href="https://www.ruangguru.com/ruangbelajar">Ruangbelajar</a></li>
<li><a href="https://pengajar.ruangguru.com/">Ruangpengajar</a></li>
<li><a href="https://www.ruangguru.com/privat">Ruangguru Privat</a></li>
<li><a href="https://www.ruangpeduli.org/" target="_blank">Ruangpeduli</a></li>
</ul>
</nav>
</div>
<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title">Bantuan & Panduan</p>
<ul type="none">
<li><a href="https://www.ruangguru.com/company-credentials">Company Credentials</a></li>
<li><a href="https://www.ruangguru.com/beasiswa">Beasiswa Ruangguru</a></li>
<li><a href="https://www.ruangguru.com/cicilan">Cicilan Ruangguru</a></li>
<li><a href="https://www.ruangguru.com/promo">Promo Ruangguru</a></li>
<li><a href="https://ticketing.ruangguru.com/help?request_type_id=459" target="_blank">Vulnerability Report</a></li>
<li><a href="https://www.ruangguru.com/bantuan#layanan">Layanan Pengaduan</a></li>
<li><a href="https://www.ruangguru.com/terms-conditions">Syarat & Ketentuan</a></li>
<li><a href="https://www.ruangguru.com/privacy-policy">Kebijakan Privasi</a></li>
<li><a href="https://www.ruangguru.com/about-us">Tentang Kami</a></li>
<li><a href="https://www.ruangguru.com/contact-us">Kontak Kami</a></li>
<li><a href="https://www.ruangguru.com/press">Press Kit</a></li>
<li><a href="https://www.ruangguru.com/bantuan">Bantuan</a></li>
<li><a href="https://career.ruangguru.com/">Karier</a></li>
</ul>
</nav>
</div>
<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title">Produk Lainnya</p>
<ul type="none">
<li><a href="https://www.brainacademy.id/" target="_blank">Brain Academy</a></li>
<li><a href="https://www.english-academy.id/" target="_blank">English Academy</a></li>
<li><a href="https://skillacademy.com/" target="_blank">Skill Academy</a></li>
<li><a href="https://www.ruangkerja.id/" target="_blank">Ruangkerja</a></li>
<li><a href="https://www.schoters.com/id/" target="_blank">Schoters</a></li>
<li><a href="https://www.kalananti.id/" target="_blank">Kalananti</a></li>
</ul>
</nav>
</div>
<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title"> Coba GRATIS Aplikasi Ruangguru</p>
<div class="download-list">
<ul>
<li>
<a target="_blank" rel="nofollow" href="https://apps.apple.com/id/app/ruangguru-solusi-belajar/id1099742206?l=id">
<img src="https://cdn-web-2.ruangguru.com/static/appstore.png" loading="lazy" alt="Button App Store Footer " />
</a>
</li>
<li>
<a target="_blank" rel="nofollow" href="https://play.google.com/store/apps/details?id=com.ruangguru.livestudents&hl=in">
<img src="https://cdn-web-2.ruangguru.com/static/googleplay.png" loading="lazy" alt="Button Google Play Footer " />
</a>
</li>
<li>
<a target="_blank" rel="nofollow" href="https://appgallery.huawei.com/#/app/C102352375">
<img src="https://cdn-web-2.ruangguru.com/static/huawei.png" loading="lazy" alt="Button AppGallery Footer " />
</a>
</li>
</ul>
</div>
</nav>
</div>
</div>
</div>
</div>
<div class="d-lg-none text-center">
<nav class="footer-menu social">
<p class="title">Ikuti Kami</p>
<a target="_blank" href="https://www.instagram.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/instagram.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/instagram.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/instagram.png" loading="lazy" alt="Logo Instagram Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.facebook.com/ruanggurucom/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/facebook.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/facebook.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/facebook.png" loading="lazy" alt="Logo Facebook Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://twitter.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/twitter.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/twitter.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/twitter.png" loading=" lazy" alt="Logo Twitter Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.youtube.com/ruangguru">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/youtube.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/youtube.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/youtube.png" loading=" lazy" alt="Logo Youtube Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.linkedin.com/company/ruangguru-com">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/linkedin.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/linkedin.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/linkedin.png" loading=" lazy" alt="Logo LinkedIn Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.tiktok.com/@ruangguru">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/tiktok.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/tiktok.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/tiktok.png" loading=" lazy" alt="Logo TikTok Footer" width="32px" height="32px" />
</picture>
</a>
</nav>
</div>
<p class="footer-copyright">
© 2026 All Rights Reserved PT. Ruang Raya Indonesia
</p>
</div>
<style>
.bantuan-container {
position: relative;
}
.bantuan-element {
position: fixed;
z-index: 999;
display: flex;
align-items: flex-end;
justify-content: flex-end;
cursor: pointer;
transition: all 0.6s ease;
}
.bantuan-top {
bottom: 11rem;
right: 2rem;
}
.bantuan-bottom {
bottom: 2rem;
right: 2rem;
}
.bantuan-top-2 {
bottom: 15rem;
right: 2rem;
}
.bantuan-top-3 {
bottom: 19rem;
right: 2rem;
}
.bantuan-bottom-2 {
bottom: 5rem;
right: 2rem;
}
.bantuan-bottom-3 {
bottom: 8rem;
right: 2rem;
}
@media (min-width: 768px) {
.bantuan-element img {
width: auto;
transition: all 0.4s ease;
}
.bantuan-top img {
width: 140px;
}
.bantuan-bottom img {
width: 140px;
}
.bantuan-top-2 img,
.bantuan-top-3 img {
width: 140px;
}
.bantuan-bottom-2 img,
.bantuan-bottom-3 img {
width: 140px;
}
.bantuan-element.clicked {
bottom: 9rem;
right: 2.5rem;
}
.bantuan-element.clicked img {
width: auto;
height: 64px;
}
}
@media (max-width: 767px) {
.bantuan-top {
bottom: 8rem;
right: 1rem;
align-items: center;
}
.bantuan-bottom {
bottom: 2rem;
right: 1.25rem;
align-items: center;
}
.bantuan-top-2 {
bottom: 12rem;
right: 1rem;
align-items: center;
}
.bantuan-top-3 {
bottom: 16rem;
right: 1rem;
align-items: center;
}
.bantuan-bottom-2 {
bottom: 5rem;
right: 1.25rem;
align-items: center;
}
.bantuan-bottom-3 {
bottom: 8rem;
right: 1.25rem;
align-items: center;
}
.bantuan-element img {
width: auto;
}
.bantuan-top img,
.bantuan-top-2 img,
.bantuan-top-3 img {
width: 96px;
}
.bantuan-bottom img,
.bantuan-bottom-2 img,
.bantuan-bottom-3 img {
width: 96px;
}
}
.bantuan-element:hover {
transform: scale(1.05);
}
.bantuan-element img {
max-width: 100%;
height: auto;
}
</style>
<div id="bantuan-divs-container" style="position: relative" data-product="ruangguru" data-table="rg_floating_icon"></div>
<script>
class FloatingDivsComponent {
constructor(product = 'ruangguru', table = 'rg_floating_icon') {
this.container = document.getElementById('bantuan-divs-container');
this.floatingElements = [];
this.product = product;
this.table = table;
// Configuration
this.config = {
baseApiUrl: 'https://gw.ruangguru.com/api/v3/rdb/p_ddgy8hjx5dxsqx/rg_banner/views/',
apiKey: 'vLyK3dJrDBRmOwueX2OJXibMkgsUbBk0WS4ua2p1',
maxElements: 2,
zIndexBase: 100,
};
// Build dynamic API URL based on table parameter
this.config.apiUrl = this.buildApiUrl();
this.init();
}
buildApiUrl() {
const baseUrl = this.config.baseApiUrl;
const tableName = this.table || 'rg_floating_icon';
const queryParams =
'offset=0&limit=99999&sort=rankPosition&where=(type,eq,floating)~and(showIn,anyof,blog)~and(hide,is,false)~and(product,eq,' +
this.product +
')&nested%5Bcta%5D%5Bfields%5D=Id,name,ctaId,imageUrl,ctaLink,targetUrl';
return `${baseUrl}${tableName}?${queryParams}`;
}
async init() {
try {
await this.fetchFloatingElements();
this.renderFloatingElements();
} catch (error) {
console.error('Failed to initialize floating divs component:', error);
}
}
async fetchFloatingElements() {
try {
const options = {
method: 'GET',
headers: {
'xc-token': this.config.apiKey || 'vLyK3dJrDBRmOwueX2OJXibMkgsUbBk0WS4ua2p1',
},
};
const urlNoco = this.config.apiUrl;
const response = await fetch(urlNoco, options);
if (!response.ok) {
throw new Error(`HTTP error! status: ${response.status}`);
}
const data = await response.json();
this.floatingElements = this.processApiResponse(data);
} catch (error) {
console.error('Error fetching floating elements:', error);
throw error;
}
}
processApiResponse(data) {
if (!data || !data.list || !Array.isArray(data.list)) {
return [];
}
console.log(data.list);
// Ensure we only get maximum 2 elements
const limitedElements = data.list.slice(0, this.config.maxElements);
return limitedElements;
}
renderFloatingElements() {
if (!this.container || this.floatingElements.length === 0) {
return;
}
// Additional safeguard: ensure we never render more than maxElements
const elementsToRender = this.floatingElements.slice(0, this.config.maxElements);
// Clean up existing elements and their event listeners
this.cleanupExistingElements();
// Clear existing content
this.container.innerHTML = '';
elementsToRender.forEach((element, index) => {
const floatingDiv = this.createFloatingDiv(element, index);
this.container.appendChild(floatingDiv);
});
}
cleanupExistingElements() {
// Clear existing elements (no need for event listener cleanup with CSS approach)
const existingElements = this.container.querySelectorAll('[data-floating-element]');
existingElements.forEach(element => {
element.remove();
});
}
createFloatingDiv(element, index) {
const div = document.createElement('div');
const cta = element.cta[0]; // Use the first CTA
// Add data attribute for cleanup tracking
div.setAttribute('data-floating-element', 'true');
// Apply CSS classes based on rankPosition
const positionClass = this.getPositionClass(element.rankPosition, index);
div.className = `bantuan-element ${positionClass}`;
div.style.zIndex = this.config.zIndexBase + index;
// Create the link and image
const link = document.createElement('a');
link.href = 'https://cta.ruangguru.com/' + cta.ctaId || '#';
link.target = '_blank';
// Add tracking attributes
link.setAttribute('data-tracking-event-type', 'landing_page__core__item_click');
link.setAttribute(
'data-tracking-context',
JSON.stringify({
product_name: this.product,
cta_action: 'redirection',
cta_action_detail: link.href,
item_type: 'floating',
item_name: element.name || 'Floating element',
item_category: 'payment',
item_position: index,
item_serial: null,
section_type: 'floating_item',
section_position: 'body',
section_name: 'floating_item',
})
);
const img = document.createElement('img');
img.src = element.imageUrl + '?h=200&convert=webp';
img.alt = element.name || 'Floating element';
img.loading = 'lazy';
// Add click tracking
link.addEventListener('click', () => {
this.trackClick(element, cta);
});
link.appendChild(img);
div.appendChild(link);
return div;
}
getPositionClass(rankPosition, index) {
// Define positioning classes based on rankPosition
if (rankPosition === 1) {
return 'bantuan-top'; // Top position
} else if (rankPosition === 2) {
return 'bantuan-bottom'; // Bottom position
} else {
// For additional elements, distribute them evenly
return `bantuan-${index % 2 === 0 ? 'top' : 'bottom'}-${Math.floor(index / 2) + 1}`;
}
}
trackClick(element, cta) {
// Implement click tracking logic here
console.log('Floating element clicked:', {
elementId: element.Id,
elementName: cta.name,
ctaId: cta.ctaId,
targetUrl: cta.targetUrl,
});
}
// Public method to manually refresh
async refresh() {
try {
await this.fetchFloatingElements();
this.renderFloatingElements();
} catch (error) {
console.error('Failed to refresh floating elements:', error);
throw error;
}
}
// Public method to get current floating elements
getFloatingElements() {
return [...this.floatingElements];
}
}
// Initialize the component when DOM is ready
document.addEventListener('DOMContentLoaded', () => {
// Get product and table parameters from data attributes
const container = document.getElementById('bantuan-divs-container');
const product = container.getAttribute('data-product') || 'ruangguru';
const table = container.getAttribute('data-table') || 'rg_floating_icon';
new FloatingDivsComponent(product, table);
});
// Export for use in other modules if needed
if (typeof module !== 'undefined' && module.exports) {
module.exports = FloatingDivsComponent;
}
</script> <div id="wp-install-nudge" style="
position: fixed;
bottom: 0rem;
right: 0;
z-index: 999;
cursor: pointer;
"></div>
<script>
(function (w, d, s, o, f, js, fjs) {
w['Sales-Nudge-Widget'] = o; w[o] = w[o] || function () { (w[o].q = w[o].q || []).push(arguments) };
js = d.createElement(s), fjs = d.getElementsByTagName(s)[0];
js.id = o; js.src = f; js.async = 1; fjs.parentNode.insertBefore(js, fjs);
}(window, document, 'script', 'wpInstallNudge', 'https://cdn-web-2.ruangguru.com/sales-nudge/6198a95130/dist/widget.js'));
wpInstallNudge('init', { targetElementId: 'wp-install-nudge', clientTarget: 'ruangguru_blog' });
</script>
<script>
// note: disabled due to auto reload page
// var lastScrollTop = 0;
// $(window).scroll(function(event){
// var st = $(this).scrollTop();
// if (st > lastScrollTop){
// $('#wp-install-nudge').slideDown( "slow", function() {});
// } else {
// $('#wp-install-nudge').slideUp( "slow", function() {});
// }
// lastScrollTop = st;
// });
// $(document).ready(function () {
// $("#wp-install-nudge").hide();
// });
$('#wp-install-nudge').click(function(){
Analytics.track("promotion__install_nudge__click",
{
user_email: "ruangguru@blog.com",
cta_link: widgetData.dataConfig.target_link
}).catch((err) => {
console.log("tracker error", err);
});
});
</script>
</footer>
<div id="__next"></div>
<script type="speculationrules">
{"prefetch":[{"source":"document","where":{"and":[{"href_matches":"\/blog\/*"},{"not":{"href_matches":["\/blog\/wp-*.php","\/blog\/wp-admin\/*","\/blog\/wp-content\/uploads\/*","\/blog\/wp-content\/*","\/blog\/wp-content\/plugins\/*","\/blog\/wp-content\/themes\/ruangguru\/*","\/blog\/*\\?(.+)"]}},{"not":{"selector_matches":"a[rel~=\"nofollow\"]"}},{"not":{"selector_matches":".no-prefetch, .no-prefetch a"}}]},"eagerness":"conservative"}]}
</script>
<script>
async function getCtaDetails(ctaIds) {
const endpoint =
" https://gw.ruangguru.com/api/v3/rdb/p_ddgy8hjx5dxsqx/CTA/views/CTA?offset=0&limit=10&where=(ctaId,in," + ctaIds.toString() + ")";
try {
const response = await fetch(endpoint, {
headers: {
"xc-token": "-hG2nBDJzSj0agSgNtcJx97M4F02y54nUMoY6plJ",
},
});
const data = await response.json();
const ctaList = data?.list || [];
const ctaMap = new Map();
for (const ctaData of ctaList) {
ctaMap.set(ctaData.ctaId, ctaData);
}
return ctaMap;
} catch (error) {
console.error("Error fetching CTA details:", error);
return new Map();
}
}
async function replaceCTA() {
const regex = /{{cta\((‘(.*?)’|“(.*?)”)\)}}/g;
const bodyHTML = document.body.innerHTML;
const matches = Array.from(bodyHTML.matchAll(regex));
const ctaIds = matches.map((match) => {
let ctaId = match[2] ?? match[3];
return ctaId;
});
const ctaMap = await getCtaDetails(ctaIds);
const replacedHTML = bodyHTML.replace(regex, (match, _inner, ctaId1, ctaId2) => {
const ctaId = ctaId1 ?? ctaId2;
const ctaData = ctaMap.get(ctaId);
if (ctaData) {
return `<a href="https://cta.ruangguru.com/${ctaData.ctaId}" target="_${ctaData.targetType}" style="position:relative;display:inline-block;">
<img src="${ctaData.imageUrl}" loading="lazy" alt="${ctaData.altText}" />
</a>`;
} else {
return match;
}
});
document.body.innerHTML = replacedHTML;
}
</script>
<meta name="author" content="Ruangguru Tech Team">
<!-- Google Tag Manager (noscript) -->
<noscript><iframe src="https://www.googletagmanager.com/ns.html?id=GTM-PVNLZFT" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript>
<!-- Tracker -->
<script type="text/javascript" src="https://cdn-web-2.ruangguru.com/landing-page-web/public/staticpages/global-assets/js/cta.js"></script>
<script src="https://unpkg.com/@dotlottie/player-component@latest/dist/dotlottie-player.mjs" type="module"></script>
</body>
</html>