Explanation Given Information: The provided polynomial is 16 + 36 x 2 + 48 x . Formula used: Follow the steps as mentioned below to compute the factorization 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, 16 + 36 x 2 + 48 x Rewrite the polynomial in descending order, 36 x 2 + 48 x + 16 Take out the largest common factor 4 as common, 36 x 2 + 48 x + 16 = 4 ( 9 x 2 + 12 x + 4 ) Now first compute the factors of 9 x 2 + 12 x + 4 , as, Take the combination of two terms, whose product is 9 x 2 , Combination of terms Product 3 x and 3 x 9 x 2 9 x and x 9 x 2 Write this combination in factor form, as, ( 3 x + ) ( 3 x + ) And ( 9 x + ) ( x + ) Take the possible pairs of two terms, whose product is 4 , Possible pairs Product of pairs 2 , 2 4 4 , 1 4 − 2 , − 2 4 − 4 , − 1 4 Here the sign of the middle term is positive and the sign of the last term is also positive. So, select the positive pairs to keep the sign of the last term positive. Form the pair to get middle term 12 by checking each possible pair via substituting the combination in the factor form, as, Trial Product Remark ( 3 x + 2 ) ( 3 x + 2 ) 9 x 2 + 6 x + 6 x + 4 = 9 x 2 + 12 x + 4 Middle term is 12 , So, this pair is correct

9th Edition

ISBN: 9780321997173

Author: Marvin L. Bittinger, Judith A. Beecher

Publisher: PEARSON

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Chapter 11.3, Problem 24ES

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Chapter 11.3, Problem 23ES

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The factorization of the polynomial 16 + 36 x 2 + 48 x .

Solution Summary: The author calculates the factorization of the polynomial 16+36x2+48x by foil method.

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Chapter 11 Solutions