Artikel ini membahas mengenai operasi suku banyak, konsep sisa dan pembagian menggunakan cara horner
Hai guys siapa nih diantara kalian yang pernah ngajarin adiknya operasi bilangan?
Kamu masih inget nggak? itu loh penjumlahan, pengurangan, perkalian dan pembagian. “Ohhh, kalau itu saya inget banget kak, karena sampe sekarang aja masih sering dipakai”
Yap betul banget! sebenarnya kamu udah ketemu operasi bilangan dari SD, dan waktu SMP kelas 7 kamu juga mulai belajar operasi aljabar kan? Jadi, setiap jenjang studi sebenarnya berkaitan dengan operasi bilangan ataupun aljabar, alasannya sederhana karena kita menerapkannya di kehidupan sehari-hari.
Di jenjang SMA kita bakal belajar operasi aljabar lagi, tapi agak beda nih. Karena yang akan dibahas kali ini mengenai operasi suku banyak. Eits, kamu udah paham konsep awal dari suku banyak belum? Kalo masih bingung tentang konsep dan cara mencari nilai suku banyak, kamu baca ini dulu deh Mempelajari Konsep dan Nilai Suku Banyak.
Materi ini seru banget untuk dipelajari, karena kita nggak cuma belajar tentang operasinya tapi konsep sisa dan juga pembagian yang nggak biasa (karena dengan bantuan Horner!) so, supaya pemahaman kamu tentang suku banyak ini makin mantap, wajib baca sampai habis ya!
Seperti operasi aljabar pada umumnya, operasi suku banyak terdiri dari penjumlahan, pengurangan, perkalian dan pembagian. Khusus untuk pembagian, akan dijelaskan dengan cara biasa yaitu bersusun ke bawah dan menggunakan cara Horner. Kita bahas satu per satu yuk!
Aturan dari penjumlahan suku banyak adalah menjumlahkan suku yang memiliki variabel serta eksponen yang sama atau menjumlahkan suku sejenis. Penjumlahan suku banyak akan menghasilkan suku banyak dengan eksponen yang sama. Misalnya ini:
Contoh Soal:
Jika f(x) = 2x3 + 4x2 + 6x + 8 dan g(x) = 7x2 – 9x – 11maka hasil dari f(x) + g(x)=…
Pembahasan:
f(x) +g(x) = (2x3 + 4x2 + 6x + 8) + (7x2 – 9x – 11)
= 2x3 + (4 + 7)x2 + (6 – 9)x + 8 -11
= 2x3 + 11x2 – 3x – 3
Jadi hasil penjumlahan f(x) dan g(x)adalah 2x3 + 11x2 – 3x – 3.
Pengurangan suku banyak artinya, mengurangkan suku dengan variabel dan eksponen yang sama atau mengubah tanda fungsi yang dikurangi. Sebenarnya, aturan pegurangan sama dengan penjumlahan, letak perbedaanya hanya pada operasinya saja. Tapi, kamu harus teliti untuk tanda plus dan minusnya ya!
Contoh Soal:
Diketahui f(x) = 5x4 + 7x2 – 3x + 5 dan g(x) = 4x4 – 8x3 + 2x + 10, tentukan hasil dari f(x) -g(x)!
Pembahasan:
f(x) – g(x) = (5x4 + 7x2 – 3x + 5) – (4x4 – 8x3 + 2x + 10)
= (5 – 4)x4 – (- 8x3) + 7x2 + (- 3 – 2)x + 5 – 10
= x4 + 8x3 + 7x2 – 5x – 5
Ingat! untuk susunan hasilnya dimulai dari eksponen tertinggi hingga terendah.
Mengalikan satu per satu suku yang ada, hingga memperoleh eksponen yang lebih tinggi atau kita menggunakan sifat distributif. Kalo kamu lupa, sifat distributif itu misalnya kaya gini :
Udah lebih ingat kan sekarang? Kalo gitu langsung ke contoh soal aja ya!
Contoh Soal:
Tentukan hasil dari perkalian dua suku banyak ini (2x2 + 6)(x3 – x + 2)!
Pembahasan:
Kamu bisa menggunakan sifat distributif, seperti ini
(2x2)(x3) + (2x2)(-x) + (2x2)(2)+(6)(x3) + (6)(-x)+(6)(2)
= 2x2+3 – 2x2+1 + 4x2+0 + 6x3 – 6x+12
= 2x5 – 2x3 + 4x2 + 6x3 – 6x+12
= 2x5 + (-2+6)x3 + 4x2 – 6x+12
= 2x5 + 4x3 + 4x2 – 6x+12
Atau kamu juga bisa coba dengan tabel seperti ini:
Seperti yang sudah disinggung sebelumnya, pembagian suku banyak bisa menggunakan cara bersusun dan Horner. Untuk cara Horner, sudah sempat dibahas dan dipakai untuk mendapatkan nilai suku banyak, tapi tenang aja untuk operasi pembagiannya bakal dibahas kok disini. Sebelum ke contoh soal, kamu harus tahu hubungan suku yang akan dibagi, pembagi dan lainnya, seperti ini:
Contoh Soal Pembagian Cara Horner:
Tentukan hasil bagi Tentukan hasil bagi f(x) = x3 – 9x + 14 dengan x-3 dengan sintetik Horner!
step 1: Tuliskan koefisien yang dibagi yaitu 1, 0 (karena x2 tidak ada dalam soal maka sama dengan 0x2),-9 dan 14 dengan pembagi yaitu 3.
step 2: Tulis koefisien suku pertama yaitu 1 di daerah hasil atau baris ke-3
step 3: Kalikan 3 dengan hasil dari step 2 yaitu 1 dan letakkan hasilnya yaitu 3 di kolom 2 baris 2. Jangan lupa jumlahkan angka 0 (koefisien suku 2) dengan 3 (hasil dari perkalian 3 dan 1) letakkan hasilnya di daerah hasil atau kolom 2 baris 3.
Ulangi step ke 3 sampai memperoleh angka paling akhir di daerah hasil.
Langkah terakhir, kita menentukan hasil bagi dan juga sisanya. Kita lihat pada daerah hasil 1, 3, 0 merupakan koefisien dari variabel x dengan derajat menurun. Sedangkan 14 adalah sisa, jadi seperti ini :
Maka, hasil bagi f(x) = x3 – 9x + 14 dengan x-3 menggunakan cara Horner adalah x2 + 3xdengan sisa 14.
Next, langsung aja yuk kita bahas cara bersusun!
Pembagian cara bersusun mirip banget konsepnya dengan pembagian bilangan waktu kita SD dulu.
Contoh Soal Pembagian Bersusun :
Hasil bagi f(x) = x3 – 9x + 14 dengan x-3 dengan cara bersusun adalah…
step 1: Susun kedua suku banyak x3 – 9x + 14 (yang kita sebut dengan “terbagi”) dengan x-3 (yang kita sebut dengan “pembagi”) tersebut menjadi seperti ini.
step 2: Bagi suku pertama terbagi yaitu x3 dengan suku pertama pembagi yaitu x.
step 3: Kalikan x2 (hasil bagi dari step 2) dengan pembagi yaitu x-3, hasilnya ditaruh di baris ke-2. Kurangkan hasil yang diperoleh dan letakan hasil di bawahnya.
step 4: Bagi -9x ( hasil dari pengurangan step 3) dengan x (suku pertama pembagi)
step 5:
Kalikan hasil dari step 4 yaitu -9 dengan pembagi yaitu x-3. Letakan hasilnya di bawah -9x + 3x2 (hasil pengurangan step 3).
Lakukan berulang step 2-5 hingga tidak ada lagi variabel yang dapat dibagi dan hanya menyisakan konstantanya yaitu 14.
Jadi, hasil bagi x3 – 9x + 14 dengan x-3 adalah x2 + 3x dengan sisanya yaitu 14.
Oke,dari perhitungan fungsi yang tadi, kita mendapatkan sisa pembagian kan?
Nah, kamu tahu nggak sih maksud dari konsep sisa? Langsung aja deh kita bahas!
Baca Juga: Mengulik Materi Logika Matematika: Konvers, Invers, dan Kontraposisi
Jadi pada konsep sisa ini, kita bisa mengetahui sisa hasil bagi secara langsung tanpa melakukan pembagian terlebih dahulu, wah jadi lebih mudah yaa! dari bentuk umum yang sudah dibahas sebelumnya yaitu:
f(x)=P(x) . H(x) + S
Jika f(x) berderajat n, P(x) berderajat m (m ≤ n) maka derajat H(x) dan S masing-masing :
- derajat H(x) adalah (n-m)
- derajat maksimum S adalah (m-1)
Contoh soal:
Tentukan sisa hasil bagi f(x) = x3 – 9x + 14 oleh x-3!
Pembahasan:
Sesuai konsep sisa, f(x) yang dibagi dengan (x-k) sisanya atau S = f(k). Maka (x-k) ⇨(x-3)
Jadi nilai k = 3, substitusikan k = 3 ke f(x) = x3 – 9x + 14
f(3) = 33 – 9(3) + 14
= 27 – 27 + 14
= 14
Kalau kita lihat hasil sisa pembagian menggunakan cara horner atau pembagian biasa hasilnya sama yaitu 14. Tapi untuk mencari nilai sisa, kalo pakai konsep sisa jauh lebih cepat.
Gimana nih udah lebih paham kan sekarang materi tentang operasi suku banyak dan konsep sisa ? Atau kamu masih mau latihan soal lagi buat menambah kemampuan kamu?
Tenang guys, aku punya solusinya! Sekarang kamu gabung ke ruangbelajar deh! Di sana kamu bisa latihan soal sepuasnya ditambah lagi pembahasan yang mudah dipahami dan pastinya bikin kamu makin semangat untuk belajar!
Referensi:
Wirodikromo, S. (2007) Matematika Jilid 2 IPA untuk kelas XI. Jakarta: Erlangga.
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<h1 class="content-title">
Operasi Suku Banyak dan Konsep Sisa | 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>November 6, 2020 • </span> <span>6 minutes read</span></p>
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<p><em><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/operasi%20suku%20banyak%20-%20header.jpg" alt="operasi suku banyak - header" width="820" style="width: 820px; display: block; margin: 0px auto;"></em></p>
<p style="text-align: justify;"><em>Artikel ini membahas mengenai operasi suku banyak, konsep sisa dan pembagian menggunakan cara horner</em></p>
<p><span id="more-5833"></span></p>
<p style="text-align: justify;">Hai guys siapa nih diantara kalian yang pernah ngajarin adiknya operasi bilangan?</p>
<p style="text-align: justify;">Kamu masih inget <em>nggak</em>? itu loh penjumlahan, pengurangan, perkalian dan pembagian. “Ohhh, kalau itu saya inget banget kak, karena sampe sekarang aja masih sering dipakai”</p>
<p style="text-align: justify;">Yap betul banget! sebenarnya kamu udah ketemu operasi bilangan dari SD, dan waktu SMP kelas 7 kamu juga mulai belajar operasi aljabar kan? Jadi, setiap jenjang studi sebenarnya berkaitan dengan operasi bilangan ataupun aljabar, alasannya sederhana karena kita menerapkannya di kehidupan sehari-hari.</p>
<p style="text-align: justify;">Di jenjang SMA kita bakal belajar operasi aljabar lagi, tapi agak beda <em>nih</em>. Karena yang akan dibahas kali ini mengenai operasi suku banyak. <em>Eits</em>, kamu udah paham konsep awal dari suku banyak belum? Kalo masih bingung tentang konsep dan cara mencari nilai suku banyak, kamu baca ini dulu <em>deh</em> <a href="/blog/konsep-dan-nilai-suku-banyak" style="font-weight: bold;" rel="noopener">Mempelajari Konsep dan Nilai Suku Banyak</a>.</p>
<p style="text-align: justify;">Materi ini seru banget untuk dipelajari, karena kita <em>nggak</em> cuma belajar tentang operasinya tapi konsep sisa dan juga pembagian yang <em>nggak</em> biasa (karena dengan bantuan Horner!) <em>so</em>, supaya pemahaman kamu tentang suku banyak ini makin mantap, wajib baca sampai habis ya!</p>
<div><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Google%20Drive%20Integration/Operasi%20Suku%20Banyak,%20Konsep%20Sisa%20-%20MTK%20Minat%2011-Nov-06-2020-09-20-20-84-AM.png" alt="operasi suku banyak" width="820" style="width: 820px; display: block; margin: 0px auto;"></div>
<div> </div>
<p style="text-align: justify;">Seperti operasi aljabar pada umumnya, operasi suku banyak terdiri dari penjumlahan, pengurangan, perkalian dan pembagian. Khusus untuk pembagian, akan dijelaskan dengan cara biasa yaitu bersusun ke bawah dan menggunakan cara Horner. Kita bahas satu per satu <em>yuk!</em></p>
<div><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Google%20Drive%20Integration/Operasi%20Suku%20Banyak,%20Konsep%20Sisa%20-%20MTK%20Minat%2011-Nov-06-2020-09-20-18-39-AM.png" alt="penjumlahan suku banyak" width="820" style="width: 820px; display: block; margin: 0px auto;"></div>
<div> </div>
<p style="text-align: justify;">Aturan dari penjumlahan suku banyak adalah <strong>menjumlahkan suku yang memiliki variabel serta eksponen yang sama atau menjumlahkan suku sejenis.</strong> Penjumlahan suku banyak akan menghasilkan suku banyak dengan eksponen yang sama. Misalnya ini:</p>
<div><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Google%20Drive%20Integration/Operasi%20Suku%20Banyak,%20Konsep%20Sisa%20-%20MTK%20Minat%2011-Nov-06-2020-09-20-18-63-AM.png" alt="penjumlahan suku banyak" width="600" style="width: 600px; display: block; margin: 0px auto;"></div>
<div> </div>
<p style="text-align: justify;"><strong>Contoh Soal:</strong></p>
<p style="text-align: justify;">Jika f(x) = 2x<sup>3 </sup>+ 4x<sup>2 </sup>+ 6x + 8 dan g(x) = 7x<sup>2 </sup>– 9x – 11maka hasil dari f(x) + g(x)=…</p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify;">f(x) +g(x) = (2x<sup>3 </sup>+ 4x<sup>2 </sup>+ 6x + 8) + (7x<sup>2 </sup>– 9x – 11)</p>
<p style="text-align: justify;">= 2x<sup>3 </sup>+ (4 + 7)x<sup>2 </sup>+ (6 – 9)x + 8 -11</p>
<p style="text-align: justify;">= 2x<sup>3 </sup>+ 11x<sup>2 </sup>– 3x – 3</p>
<p style="text-align: justify;">Jadi hasil penjumlahan f(x) dan g(x)adalah 2x<sup>3 </sup>+ 11x<sup>2 </sup>– 3x – 3.</p>
<div><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Google%20Drive%20Integration/Operasi%20Suku%20Banyak,%20Konsep%20Sisa%20-%20MTK%20Minat%2011-Nov-06-2020-09-20-20-36-AM.png" alt="pengurangan suku banyak" width="820" style="width: 820px; display: block; margin: 0px auto;"></div>
<div> </div>
<p style="text-align: justify;">Pengurangan suku banyak artinya, <strong>mengurangkan suku dengan variabel dan eksponen yang sama atau mengubah tanda fungsi yang dikurangi. Sebenarnya, aturan pegurangan sama dengan penjumlahan, letak perbedaanya hanya pada operasinya saja.</strong> Tapi, kamu harus teliti untuk tanda plus dan minusnya ya!</p>
<p style="text-align: justify;"><strong>Contoh Soal:</strong></p>
<p style="text-align: justify;">Diketahui f(x) = 5x<sup>4 </sup>+ 7x<sup>2 </sup>– 3x + 5 dan g(x) = 4x<sup>4 </sup>– 8x<sup>3 </sup>+ 2x + 10, tentukan hasil dari f(x) -g(x)!</p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify;">f(x) – g(x) = (5x<sup>4 </sup>+ 7x<sup>2 </sup>– 3x + 5) – (4x<sup>4 </sup>– 8x<sup>3 </sup>+ 2x + 10)</p>
<p style="text-align: justify;">= (5 – 4)x<sup>4 </sup>– (- 8x<sup>3</sup>) + 7x<sup>2 </sup>+ (- 3 – 2)x + 5 – 10</p>
<p style="text-align: justify;">= x<sup>4 </sup>+ 8x<sup>3 </sup>+ 7x<sup>2 </sup>– 5x – 5</p>
<p style="text-align: justify;"><strong>Ingat!</strong> <strong>untuk</strong> <strong>susunan hasilnya</strong> <strong>dimulai dari eksponen tertinggi hingga terendah</strong>.</p>
<div><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Google%20Drive%20Integration/Operasi%20Suku%20Banyak,%20Konsep%20Sisa%20-%20MTK%20Minat%2011-Nov-06-2020-09-20-18-50-AM.png" alt="perkalian suku banyak" width="820" style="width: 820px; display: block; margin: 0px auto;"></div>
<div> </div>
<p style="text-align: justify;"><strong>Mengalikan satu per satu suku yang ada, hingga memperoleh eksponen yang lebih tinggi atau kita menggunakan sifat distributif.</strong> Kalo kamu lupa, sifat distributif itu misalnya <em>kaya gini</em> :</p>
<div><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Google%20Drive%20Integration/Operasi%20Suku%20Banyak,%20Konsep%20Sisa%20-%20MTK%20Minat%2011-2.png" alt="perkalian suku banyak" width="600" style="width: 600px; display: block; margin: 0px auto;"></div>
<div> </div>
<p style="text-align: justify;">Udah lebih ingat kan sekarang? Kalo gitu langsung ke contoh soal aja ya!</p>
<p style="text-align: justify;"><strong>Contoh Soal:</strong></p>
<p style="text-align: justify;">Tentukan hasil dari perkalian dua suku banyak ini (2x<sup>2 </sup>+ 6)(x<sup>3 </sup>– x + 2)!</p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify;">Kamu bisa menggunakan sifat distributif, seperti ini</p>
<p style="text-align: justify;">(2x<sup>2</sup>)(x<sup>3</sup>) + (2x<sup>2</sup>)(-x) + (2x<sup>2</sup>)(2)+(6)(x<sup>3</sup>) + (6)(-x)+(6)(2)</p>
<p style="text-align: justify;">= 2x<sup>2+3 </sup>– 2x<sup>2+1 </sup>+ 4x<sup>2+0 </sup>+ 6x<sup>3 </sup>– 6x+12</p>
<p style="text-align: justify;">= 2x<sup>5 </sup>– 2x<sup>3 </sup>+ 4x<sup>2 </sup>+ 6x<sup>3 </sup>– 6x+12</p>
<p style="text-align: justify;">= 2x<sup>5 </sup>+ (-2+6)x<sup>3 </sup>+ 4x<sup>2 </sup>– 6x+12</p>
<p style="text-align: justify;">= 2x<sup>5 </sup>+ 4x<sup>3 </sup>+ 4x<sup>2 </sup>– 6x+12</p>
<p style="text-align: justify;">Atau kamu juga bisa coba dengan tabel seperti ini:</p>
<div><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Google%20Drive%20Integration/Operasi%20Suku%20Banyak,%20Konsep%20Sisa%20-%20MTK%20Minat%2011-Nov-06-2020-09-20-19-53-AM.png" alt="perkalian suku banyak" width="300" style="width: 300px; display: block; margin: 0px auto;"></div>
<div> </div>
<div><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Google%20Drive%20Integration/Operasi%20Suku%20Banyak,%20Konsep%20Sisa%20-%20MTK%20Minat%2011-Nov-06-2020-09-20-19-66-AM.png" alt="pembagian suku banyak" width="820" style="width: 820px; display: block; margin: 0px auto;"></div>
<div> </div>
<p style="text-align: justify;">Seperti yang sudah disinggung sebelumnya, <strong>pembagian suku banyak bisa menggunakan cara bersusun dan Horner.</strong> Untuk cara Horner, sudah sempat dibahas dan dipakai untuk mendapatkan nilai suku banyak, tapi tenang aja untuk operasi pembagiannya bakal dibahas kok disini. Sebelum ke contoh soal, kamu harus tahu hubungan suku yang akan dibagi, pembagi dan lainnya, seperti ini:</p>
<div><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/operasi%20suku%20banyak%20-%20terserah%20d.jpg" alt="pembagian suku banyak" width="600" style="width: 600px; display: block; margin: 0px auto;"></div>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;"><strong>Contoh Soal Pembagian Cara Horner:</strong></p>
<p style="text-align: justify;">Tentukan hasil bagi Tentukan hasil bagi f(x) = x<sup>3 </sup>– 9x + 14 dengan x-3 dengan sintetik Horner!</p>
<p style="text-align: justify;"><strong>step 1: </strong>Tuliskan koefisien yang dibagi yaitu 1, 0 (karena x<sup>2</sup> tidak ada dalam soal maka sama dengan 0x<sup>2</sup>),-9 dan 14 dengan pembagi yaitu 3.</p>
<div><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Google%20Drive%20Integration/Operasi%20Suku%20Banyak,%20Konsep%20Sisa%20-%20MTK%20Minat%2011-Nov-06-2020-09-20-20-48-AM.png" alt="" width="300" style="width: 300px; display: block; margin: 0px auto;"></div>
<p style="text-align: justify;"><strong>step 2:</strong> Tulis koefisien suku pertama yaitu 1 di daerah hasil atau baris ke-3</p>
<div><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Google%20Drive%20Integration/Operasi%20Suku%20Banyak,%20Konsep%20Sisa%20-%20MTK%20Minat%2011-Nov-06-2020-09-20-18-30-AM.png" alt="" width="300" style="width: 300px; display: block; margin: 0px auto;"></div>
<p style="text-align: justify;"><strong>step 3: </strong>Kalikan 3 dengan hasil dari step 2 yaitu 1 dan letakkan hasilnya yaitu 3 di kolom 2 baris 2. Jangan lupa jumlahkan angka 0 (koefisien suku 2) dengan 3 (hasil dari perkalian 3 dan 1) letakkan hasilnya di daerah hasil atau kolom 2 baris 3.</p>
<div><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Google%20Drive%20Integration/Operasi%20Suku%20Banyak,%20Konsep%20Sisa%20-%20MTK%20Minat%2011-Nov-06-2020-09-20-18-96-AM.png" alt="" width="300" style="width: 300px; display: block; margin: 0px auto;"></div>
<p style="text-align: justify;">Ulangi step ke 3 sampai memperoleh angka paling akhir di daerah hasil.</p>
<div><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Google%20Drive%20Integration/Operasi%20Suku%20Banyak,%20Konsep%20Sisa%20-%20MTK%20Minat%2011-Nov-06-2020-09-20-20-58-AM.png" alt="" width="300" style="width: 300px; display: block; margin: 0px auto;"></div>
<p style="text-align: justify;">Langkah terakhir, kita menentukan <strong>hasil bagi dan juga sisanya</strong>. Kita lihat pada daerah hasil 1, 3, 0 merupakan koefisien dari variabel x dengan derajat menurun. Sedangkan 14 adalah sisa, jadi seperti ini :</p>
<div><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Google%20Drive%20Integration/Operasi%20Suku%20Banyak,%20Konsep%20Sisa%20-%20MTK%20Minat%2011-1.png" alt="" width="300" style="width: 300px; display: block; margin: 0px auto;"></div>
<p style="text-align: justify;">Maka, hasil bagi f(x) = x<sup>3</sup> – 9x + 14 dengan x-3 menggunakan cara Horner adalah x<sup>2</sup> + 3xdengan sisa 14.</p>
<p style="text-align: justify;"><em>Next,</em> langsung aja yuk kita bahas cara bersusun!</p>
<p style="text-align: justify;"><strong>Pembagian cara bersusun mirip banget konsepnya dengan pembagian bilangan waktu kita SD dulu</strong>.</p>
<p style="text-align: justify;">Contoh Soal Pembagian Bersusun :</p>
<p style="text-align: justify;">Hasil bagi f(x) = x<sup>3</sup> – 9x + 14 dengan x-3 dengan cara bersusun adalah…</p>
<p style="text-align: justify;"><strong>step 1: </strong>Susun kedua suku banyak x<sup>3</sup> – 9x + 14 (yang kita sebut dengan “terbagi”) dengan x-3 (yang kita sebut dengan “pembagi”) tersebut menjadi seperti ini.</p>
<div><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Google%20Drive%20Integration/Operasi%20Suku%20Banyak,%20Konsep%20Sisa%20-%20MTK%20Minat%2011.png" alt="" width="300" style="width: 300px; display: block; margin: 0px auto;"></div>
<p style="text-align: justify;"><strong>step 2: </strong> Bagi suku pertama terbagi yaitu x<sup>3</sup> dengan suku pertama pembagi yaitu x.</p>
<div><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Google%20Drive%20Integration/Operasi%20Suku%20Banyak,%20Konsep%20Sisa%20-%20MTK%20Minat%2011-Nov-06-2020-09-20-20-20-AM.png" alt="" width="300" style="width: 300px; display: block; margin: 0px auto;"></div>
<p style="text-align: justify;"><strong>step 3:</strong> Kalikan x<sup>2</sup> (hasil bagi dari step 2) dengan pembagi yaitu x-3, hasilnya ditaruh di baris ke-2. Kurangkan hasil yang diperoleh dan letakan hasil di bawahnya.</p>
<div><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Google%20Drive%20Integration/Operasi%20Suku%20Banyak,%20Konsep%20Sisa%20-%20MTK%20Minat%2011-Nov-06-2020-09-20-18-18-AM.png" alt="" width="300" style="width: 300px; display: block; margin: 0px auto;"></div>
<p style="text-align: justify;"><strong>step 4:</strong> Bagi -9x ( hasil dari pengurangan step 3) dengan x (suku pertama pembagi)</p>
<div><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Google%20Drive%20Integration/Operasi%20Suku%20Banyak,%20Konsep%20Sisa%20-%20MTK%20Minat%2011-Nov-06-2020-09-20-17-94-AM.png" alt="" width="300" style="width: 300px; display: block; margin: 0px auto;"></div>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;"><strong>step 5:</strong></p>
<p style="text-align: justify;">Kalikan hasil dari step 4 yaitu -9 dengan pembagi yaitu x-3. Letakan hasilnya di bawah -9x + 3x<sup>2 </sup>(hasil pengurangan step 3).</p>
<div><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/operasi%20suku%20banyak%20-%20rumus%2011.jpg" alt="operasi suku banyak - rumus 11" width="300" style="width: 300px; display: block; margin: 0px auto;"></div>
<p style="text-align: justify;">Lakukan berulang step 2-5 hingga tidak ada lagi variabel yang dapat dibagi dan hanya menyisakan konstantanya yaitu 14.</p>
<div><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Google%20Drive%20Integration/Operasi%20Suku%20Banyak,%20Konsep%20Sisa%20-%20MTK%20Minat%2011-Nov-06-2020-09-20-20-72-AM.png" alt="" width="300" style="width: 300px; display: block; margin: 0px auto;"></div>
<p style="text-align: justify;"> </p>
<p style="text-align: justify;">Jadi, hasil bagi x<sup>3</sup> – 9x + 14 dengan x-<sup>3</sup> adalah x<sup>2 </sup>+ 3x dengan sisanya yaitu 14.</p>
<p style="text-align: justify;">Oke,dari perhitungan fungsi yang tadi, kita mendapatkan sisa pembagian kan?</p>
<p style="text-align: justify;"><em>Nah,</em> kamu tahu nggak <em>sih</em> maksud dari konsep sisa? Langsung aja deh kita bahas!</p>
<p style="text-align: justify;"><strong>Baca Juga: <a href="/mengulik-materi-logika-matematika" rel="noopener" target="_blank">Mengulik Materi Logika Matematika: Konvers, Invers, dan Kontraposisi</a></strong> </p>
<div><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Google%20Drive%20Integration/Operasi%20Suku%20Banyak,%20Konsep%20Sisa%20-%20MTK%20Minat%2011-4.png" alt="konsep sisa" width="820" style="width: 820px; display: block; margin: 0px auto;"></div>
<div style="text-align: justify;"> </div>
<p style="text-align: justify;">Jadi pada <strong>konsep sisa ini, kita bisa mengetahui sisa hasil bagi secara langsung tanpa melakukan pembagian terlebih dahulu,</strong> wah jadi lebih mudah yaa! dari bentuk umum yang sudah dibahas sebelumnya yaitu:</p>
<p style="text-align: center; font-size: 20px;"><em><strong>f(x)=P(x) . H(x) + S</strong></em></p>
<p style="text-align: justify;"><strong>Jika f(x) berderajat n, P(x) berderajat m (m ≤ n) maka derajat H(x) dan S masing-masing :</strong></p>
<ul style="text-align: justify;">
<li><strong>derajat H(x) adalah (n-m)</strong></li>
<li><strong>derajat maksimum S adalah (m-1)</strong></li>
</ul>
<div><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Google%20Drive%20Integration/Operasi%20Suku%20Banyak,%20Konsep%20Sisa%20-%20MTK%20Minat%2011-Nov-06-2020-09-20-19-15-AM.png" alt="" width="600" style="width: 600px; display: block; margin: 0px auto;"></div>
<div> </div>
<p style="text-align: justify;"><strong>Contoh soal:</strong></p>
<p style="text-align: justify;">Tentukan sisa hasil bagi f(x) = x<sup>3</sup> – 9x + 14 oleh x-3!</p>
<p style="text-align: justify;"><strong>Pembahasan:</strong></p>
<p style="text-align: justify;">Sesuai konsep sisa, f(x) yang dibagi dengan (x-k) sisanya atau S = f(k). Maka (x-k) ⇨(x-3)</p>
<p style="text-align: justify;">Jadi nilai k = 3, substitusikan k = 3 ke f(x) = x<sup>3 </sup>– 9x + 14</p>
<p style="text-align: justify;">f(3) = 3<sup>3 </sup>– 9(3) + 14</p>
<p style="text-align: justify;">= 27 – 27 + 14</p>
<p style="text-align: justify;">= 14</p>
<p style="text-align: justify;">Kalau kita lihat hasil sisa pembagian menggunakan cara horner atau pembagian biasa hasilnya sama yaitu 14. Tapi untuk mencari nilai sisa, kalo pakai konsep sisa jauh lebih cepat.</p>
<p style="text-align: justify;">Gimana <em>nih</em> udah lebih paham kan sekarang materi tentang operasi suku banyak dan konsep sisa ? Atau kamu masih mau latihan soal lagi buat menambah kemampuan kamu?</p>
<p style="text-align: justify;">Tenang <em>guys</em>, aku punya solusinya! Sekarang kamu gabung ke <a href="https://ruangguru.com/ruangbelajar" rel="noopener"><strong>ruangbelajar</strong></a> deh! Di sana kamu bisa latihan soal sepuasnya ditambah lagi pembahasan yang mudah dipahami dan pastinya bikin kamu makin semangat untuk belajar!</p>
<p style="text-align: center;"><a href="https://link.ruangguru.com/blPk/eaff0eb9" target="_blank" style="text-align: center;" class="rg-cta" rel="noopener"><img fetchpriority="high" decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/cta/0ec4a2df-db2e-4ae1-8473-692756dcb684.jpeg" width="822" height="200" alt="IDN CTA Blog ruangbelajar Ruangguru" /></a></p>
<p style="text-align: justify;"><strong>Referensi:</strong></p>
<p style="text-align: justify;">Wirodikromo, S. (2007) Matematika Jilid 2 IPA untuk kelas XI. Jakarta: Erlangga.</p>
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<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>
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<li><a href="https://www.ruangguru.com/for-kids/kursus">Kursus for Kids</a></li>
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<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>
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<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">
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<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">
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<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">
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</picture>
</a>
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<picture>
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</a>
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<picture>
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</a>
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<picture>
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</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>