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2026-01-01
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<p>116 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 is a polynomial that can be found using polynomial division techniques. We will learn about the quotient of (x³ + 3x² + 5x + 3) ÷ (x + 1) below.</p>
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<p>The result we get when we divide one polynomial by another is called the quotient. The quotient is a polynomial that can be found using polynomial division techniques. We will learn about the quotient of (x³ + 3x² + 5x + 3) ÷ (x + 1) below.</p>
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<h2>What is the Quotient of (x³ + 3x² + 5x + 3) ÷ (x + 1)?</h2>
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<h2>What is the Quotient of (x³ + 3x² + 5x + 3) ÷ (x + 1)?</h2>
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<p>To find the<a>quotient</a><a>of</a>(x³ + 3x² + 5x + 3) ÷ (x + 1), 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><a>of</a>(x³ + 3x² + 5x + 3) ÷ (x + 1), 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>Divide the first<a>term</a>of the<a>dividend</a>by the first term of the<a>divisor</a>. Here, divide x³ by x to get x².</p>
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<p><strong>Step 1:</strong>Divide the first<a>term</a>of the<a>dividend</a>by the first term of the<a>divisor</a>. Here, divide x³ by x to get x².</p>
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<p><strong>Step 2:</strong>Multiply the entire divisor (x + 1) by the result from Step 1 (x²) and subtract the result from the original polynomial. You will get a new polynomial: (3x² + 5x + 3) - (x²)(x + 1) = 2x² + 5x + 3.</p>
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<p><strong>Step 2:</strong>Multiply the entire divisor (x + 1) by the result from Step 1 (x²) and subtract the result from the original polynomial. You will get a new polynomial: (3x² + 5x + 3) - (x²)(x + 1) = 2x² + 5x + 3.</p>
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<p><strong>Step 3:</strong>Repeat the process with the new polynomial. Divide the first term of the new polynomial (2x²) by the first term of the divisor (x) to get 2x.</p>
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<p><strong>Step 3:</strong>Repeat the process with the new polynomial. Divide the first term of the new polynomial (2x²) by the first term of the divisor (x) to get 2x.</p>
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<p><strong>Step 4:</strong>Multiply the entire divisor by the result from Step 3 (2x) and subtract from the current polynomial: (2x² + 5x + 3) - (2x)(x + 1) = 3x + 3.</p>
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<p><strong>Step 4:</strong>Multiply the entire divisor by the result from Step 3 (2x) and subtract from the current polynomial: (2x² + 5x + 3) - (2x)(x + 1) = 3x + 3.</p>
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<p><strong>Step 5:</strong>Divide the first term of the remaining polynomial (3x) by the first term of the divisor (x) to get 3.</p>
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<p><strong>Step 5:</strong>Divide the first term of the remaining polynomial (3x) by the first term of the divisor (x) to get 3.</p>
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<p><strong>Step 6:</strong>Multiply the entire divisor by the result from Step 5 (3) and subtract from the current polynomial: (3x + 3) - (3)(x + 1) = 0. The quotient is x² + 2x + 3.</p>
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<p><strong>Step 6:</strong>Multiply the entire divisor by the result from Step 5 (3) and subtract from the current polynomial: (3x + 3) - (3)(x + 1) = 0. The quotient is x² + 2x + 3.</p>
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<h2>Important Glossaries of Quotient of (x³ + 3x² + 5x + 3) ÷ (x + 1)</h2>
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<h2>Important Glossaries of Quotient of (x³ + 3x² + 5x + 3) ÷ (x + 1)</h2>
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<ul><li><strong>Quotient:</strong>The result of dividing one polynomial by another.</li>
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<ul><li><strong>Quotient:</strong>The result of dividing one polynomial by another.</li>
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</ul><ul><li><strong>Dividend:</strong>The polynomial that is being divided.</li>
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</ul><ul><li><strong>Dividend:</strong>The polynomial that is being divided.</li>
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</ul><ul><li><strong>Divisor:</strong>The polynomial by which the dividend is divided.</li>
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</ul><ul><li><strong>Divisor:</strong>The polynomial by which the dividend is divided.</li>
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</ul><ul><li><strong>Polynomial Division:</strong>A method similar to long division for dividing polynomials.</li>
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</ul><ul><li><strong>Polynomial Division:</strong>A method similar to long division for dividing polynomials.</li>
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</ul><ul><li><strong>Remainder:</strong>The part of the dividend that is left after the division process, if any.</li>
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</ul><ul><li><strong>Remainder:</strong>The part of the dividend that is left after the division process, if any.</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>