Explanation Given Information: The expression, − 4 x + 3 x 3 + 2 x − 1 . Formula used: 1. Following steps are used to divide a polynomial with missing terms: Step 1: Polynomial must be in descending order. Step 2: Use 0 as the coefficient for each missing term. Step 3: Divide the term with the greatest power of dividend by the term with the highest power of divisor; then multiply the resultant term with the divisor. Step 4: Subtract and bring down the next term. Step 5: Repeat the Steps 2 and 3 until there are no terms to bring down. Step 6: The final answer after the subtract step is the remainder. If the remainder is non-zero, then write it as the numerator of a fraction with the divisor as remainder which makes the answer not a polynomial. 2. Distributive property: a ( b + c ) = a ⋅ b + a ⋅ c Calculation: Consider the expression, − 4 x + 3 x 3 + 2 x − 1 . Step 1: Here, the dividend, ( − 4 x + 3 x 3 + 2 ) is missing the x 2 term. Therefore, use 0 as the coefficient for the missing term. Thus, − 4 x + 3 x 3 + 2 = 3 x 3 + 0 x 2 − 4 x + 2 Step 2: Divide 3 x 3 by x . That is, 3 x 3 x = 3 x 2 . Distribute 3 x 2 with ( x − 1 ) . That is, 3 x 2 ( x − 1 ) = 3 x 3 − 3 x 2 . Step 3: Subtract ( 3 x 3 − 3 x 2 ) from ( 3 x 3 + 0 x 2 ) . Then bring down the next term − 4 x . Step 4: Divide 3 x 2 by x . That is, 3 x 2 x = 3 x . Distribute 3 x with ( x − 1 ) . That is, 3 x ( x − 1 ) = 3 x 2 − 3 x . Step 5: Subtract ( 3 x 2 − 3 x ) from ( 3 x 2 − 4 x ) . Then bring down the next term 2. Step 6: Divide − x by x . That is, − x x = − 1 . Distribute − 1 with ( x − 1 ) . That is, − 1 ( x − 1 ) = − x + 1 . Step 7: Subtract ( − x + 1 ) from ( − x + 2 )

Beginning and Intermediate Algebra (6th Edition)

6th Edition

ISBN: 9780321969163

Author: Margaret L. Lial, John Hornsby, Terry McGinnis

Publisher: PEARSON

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Chapter 4.7, Problem 65E

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To calculate: The value of the expression, −4x+3x3+2x−1 using long division process.

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Chapter 4.7, Problem 64E

Chapter 4.7, Problem 66E

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Chapter 4 Solutions

Beginning and Intermediate Algebra (6th Edition)

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The value of the expression, − 4 x + 3 x 3 + 2 x − 1 using long division process.

Solution Summary: The author explains how to divide a polynomial with missing terms using the following steps.

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To calculate: The value of the expression, −4x+3x3+2x−1 using long division process.

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Chapter 4 Solutions