Explanation Given Information: The expression, 1000 x 6 + 1 10 x 2 + 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, 1000 x 6 + 1 10 x 2 + 1 . First arrange the dividend in descending powers and use 0 as the coefficient of the missing term. That is, divide the polynomial 1000 x 6 + 0 x 4 + 0 x 2 + 1 by 10 x 2 + 1 . In the polynomial, 1000 x 6 + 0 x 4 + 0 x 2 + 1 , the term 1000 x 6 divided by 10 x 2 equals to 1000 x 6 10 x 2 = 100 x 4 . Distribute 100 x 4 with ( 10 x 2 + 0 x + 1 ) , which is 100 x 4 ( 10 x 2 + 0 x + 1 ) = 1000 x 6 + 100 x 4 , 10 x 2 + 0 x + 1 100 x 4 1000 x 6 + 0 x 4 + 0 x 2 + 0 x + 1 1000 x 6 + 100 x 4 _ Subtract the polynomial and then bring down the next term. To subtract the polynomials, change the sign of the second polynomial 1000 x 6 + 100 x 4 and then add, 10 x 2 + 0 x + 1 100 x 4 1000 x 6 + 0 x 4 + 0 x 2 + 0 x + 1 1000 x 6 + 100 x 4 _ − 100 x 4 + 0 x 2 In the polynomial, − 100 x 4 + 0 x 2 , the term − 100 x 4 divided by 10 x 2 equals to − 100 x 4 10 x 2 = − 10 x 2 . Distribute – 10 x 2 with 10 x 2 + 0 x + 1 , which is − 10 x 2 ( 10 x 2 + 0 x + 1 ) = − 100 x 4 − 10 x 2 , 10 x 2 + 0 x + 1 100 x 4 1000 x 6 + 0 x 4 + 0 x 2 + 0 x + 1 1000 x 6 + 100 x 4 _ − 100 x 4 +

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ISBN: 9781323910528

Author: Lial

Publisher: PEARSON C

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Chapter 4, Problem 86RE

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To calculate: The simplified form of the expression, 1000x6+110x2+1.

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Chapter 4, Problem 85RE

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The simplified form of the expression, 1000 x 6 + 1 10 x 2 + 1 .

Solution Summary: The author explains how to divide a polynomial with missing terms.

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To calculate: The simplified form of the expression, 1000x6+110x2+1.

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