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2026-01-01
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2026-02-28
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<p>125 Learners</p>
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<p>Last updated on<strong>October 4, 2025</strong></p>
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<p>Last updated on<strong>October 4, 2025</strong></p>
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<p>The result we get when we divide one polynomial by another is called the quotient. The quotient can be a polynomial or a rational expression, depending on the polynomials involved. We will learn about the quotient of (x³ + 6x² + 11x + 6) ÷ (x² + 4x + 3)x + 2x - 2x + 10x + 6 below.</p>
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<p>The result we get when we divide one polynomial by another is called the quotient. The quotient can be a polynomial or a rational expression, depending on the polynomials involved. We will learn about the quotient of (x³ + 6x² + 11x + 6) ÷ (x² + 4x + 3)x + 2x - 2x + 10x + 6 below.</p>
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<h2>What is the Quotient of (x³ + 6x² + 11x + 6) ÷ (x² + 4x + 3)x + 2x - 2x + 10x + 6?</h2>
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<h2>What is the Quotient of (x³ + 6x² + 11x + 6) ÷ (x² + 4x + 3)x + 2x - 2x + 10x + 6?</h2>
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<p>To find the<a>quotient</a>of (x³ + 6x² + 11x + 6) ÷ (x² + 4x + 3), we can follow the steps given below. These steps make the<a>polynomial division</a>process simple.</p>
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<p>To find the<a>quotient</a>of (x³ + 6x² + 11x + 6) ÷ (x² + 4x + 3), we can follow the steps given below. These steps make the<a>polynomial division</a>process simple.</p>
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<p><strong>Step 1:</strong>Identify the<a>divisor</a>and<a>dividend</a>. In this case, the dividend is x³ + 6x² + 11x + 6, and the divisor is x² + 4x + 3.</p>
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<p><strong>Step 1:</strong>Identify the<a>divisor</a>and<a>dividend</a>. In this case, the dividend is x³ + 6x² + 11x + 6, and the divisor is x² + 4x + 3.</p>
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<p><strong>Step 2:</strong>Divide the leading<a>term</a>of the dividend (x³) by the leading term of the divisor (x²) to get the first term of the quotient, which is x.</p>
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<p><strong>Step 2:</strong>Divide the leading<a>term</a>of the dividend (x³) by the leading term of the divisor (x²) to get the first term of the quotient, which is x.</p>
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<p><strong>Step 3:</strong>Multiply the entire divisor by the first term of the quotient (x) and subtract from the dividend to find the new dividend: (x³ + 6x² + 11x + 6) - (x³ + 4x² + 3x) = 2x² + 8x + 6.</p>
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<p><strong>Step 3:</strong>Multiply the entire divisor by the first term of the quotient (x) and subtract from the dividend to find the new dividend: (x³ + 6x² + 11x + 6) - (x³ + 4x² + 3x) = 2x² + 8x + 6.</p>
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<p><strong>Step 4:</strong>Repeat the process with the new dividend. Divide 2x² by x² to get the next term of the quotient, which is 2.</p>
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<p><strong>Step 4:</strong>Repeat the process with the new dividend. Divide 2x² by x² to get the next term of the quotient, which is 2.</p>
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<p><strong>Step 5:</strong>Multiply the entire divisor by 2 and subtract from the new dividend: (2x² + 8x + 6) - (2x² + 8x + 6) = 0.</p>
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<p><strong>Step 5:</strong>Multiply the entire divisor by 2 and subtract from the new dividend: (2x² + 8x + 6) - (2x² + 8x + 6) = 0.</p>
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<p><strong>Step 6:</strong>The quotient is x + 2, and since the<a>remainder</a>is 0, it confirms the division is exact.</p>
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<p><strong>Step 6:</strong>The quotient is x + 2, and since the<a>remainder</a>is 0, it confirms the division is exact.</p>
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<h3>Explore Our Programs</h3>
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<h3>Explore Our Programs</h3>
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<h2>Important Glossaries of Polynomial Division</h2>
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<h2>Important Glossaries of Polynomial Division</h2>
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<ul><li><strong>Quotient:</strong>The result obtained when dividing one polynomial by another.</li>
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<ul><li><strong>Quotient:</strong>The result obtained when dividing one polynomial by another.</li>
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</ul><ul><li><strong>Dividend:</strong>The polynomial being divided.</li>
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</ul><ul><li><strong>Dividend:</strong>The polynomial being divided.</li>
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</ul><ul><li><strong>Divisor:</strong>The polynomial by which we divide.</li>
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</ul><ul><li><strong>Divisor:</strong>The polynomial by which we divide.</li>
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</ul><ul><li><strong>Leading term:</strong>The term in a polynomial with the highest power of the variable.</li>
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</ul><ul><li><strong>Leading term:</strong>The term in a polynomial with the highest power of the variable.</li>
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</ul><ul><li><strong>Polynomial division:</strong>The process used to divide one polynomial by another, similar to long division with numbers.</li>
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</ul><ul><li><strong>Polynomial division:</strong>The process used to divide one polynomial by another, similar to long division with numbers.</li>
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</ul><h2>Jaskaran Singh Saluja</h2>
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</ul><h2>Jaskaran Singh Saluja</h2>
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<h3>About the Author</h3>
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<h3>About the Author</h3>
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<p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>
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<p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>
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<h3>Fun Fact</h3>
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<h3>Fun Fact</h3>
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<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>
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<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>