Explanation Given Information: The provided polynomial is 3 x 6 a − 2 x 3 a − 1 . Formula used: Follow the steps as mentioned below to compute the factor of a polynomial a x 2 + b x + c when a ≠ 1 by foil method. Step 1: Take the largest common factor as common, if possible. Step 2: Find the two first terms in a combination whose product will give a x 2 which will represent “ F” in the FOIL. Step 3: Find the two last terms in a combination whose product will give c which will represent “ L” in the FOIL. Step 4: Take the outer product by multiplying first and the last term obtained from step 2 and 3 also take the inner product by multiplying reaming inner terms obtained from step 2 and 3 then take the sum of results to get the value of b x which will represent “OI” in the FOIL. Step 5: Check the result by multiplication. Calculation: Consider the provided polynomial, 3 x 6 a − 2 x 3 a − 1 Take the combination of two terms, whose product is 3 x 6 a , Combination of terms Product 3 x 3 a and x 3 a 3 x 6 a Write this combination in factor form, as, ( 3 x 3 a + ) ( x 3 a + ) Take the possible pairs of two terms, whose product is − 1 , Possible pairs Product of pairs 1 , − 1 − 1 − 1 , 1 − 1 Form the pair to get middle term − 2 x 3 a by checking each possible pair via substituting the combination in the factor form, as, Trial Product Remark ( 3 x 3 a + 1 ) ( x 3 a − 1 ) 3 x 6 a − 3 x 3 a + x 3 a − 1 = 3 x 6 a − 2 x 3 a − 1 Middle term is − 2 x 3 a , So, this pair is correct

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ISBN: 9780321997173

Author: Marvin L. Bittinger, Judith A. Beecher

Publisher: PEARSON

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Chapter 11.3, Problem 87ES

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Chapter 11.3, Problem 86ES

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Chapter 11 Solutions

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The factor of the polynomial 3 x 6 a − 2 x 3 a − 1 .

Solution Summary: The author explains how to calculate the factor of a polynomial by foil method.

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To calculate: The factor of the polynomial 3x6a−2x3a−1.

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Chapter 11 Solutions