Explanation Given Information: The provided polynomial is 12 x 2 + 28 x − 24 . 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, 12 x 2 + 28 x − 24 Take out the largest common factor 4 as common, 12 x 2 + 28 x − 24 = 4 ( 3 x 2 + 7 x − 6 ) Now first compute the factors of 3 x 2 + 7 x − 6 , as, Take the combination of two terms, whose product is 3 x 2 , Combination of terms Product 3 x and x 3 x 2 Write this combination in factor form, as, ( 3 x + ) ( x + ) Take the possible pairs of two terms, whose product is − 6 , Possible pairs Product of pairs 2 , − 3 − 6 − 2 , 3 − 6 3 , − 2 − 6 − 3 , 2 − 6 1 , − 6 − 6 − 1 , 6 − 6 6 , − 1 − 6 − 6 , 1 − 6 Form the pair to get middle term 7 by checking each possible pair via substituting the combination in the factor form, as, Trial Product Remark ( 3 x + 2 ) ( x − 3 ) 3 x 2 − 9 x + 2 x − 6 = 3 x 2 − 7 x − 6 Middle term is not 7 , So, this pair is wrong. ( 3 x − 2 ) ( x + 3 ) 3 x 2 + 9 x − 2 x − 6 = 3 x 2 + 7 x − 6 Middle term is 7 , So, this pair is correct. ( 3 x + 3 ) ( x − 2 ) 3 x 2 − 6 x + 3 x − 6 = 3 x 2 − 3 x − 6 Middle term is not 7 , So, this pair is wrong

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ISBN: 9780321997173

Author: Marvin L. Bittinger, Judith A. Beecher

Publisher: PEARSON

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Chapter 11.3, Problem 31ES

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Chapter 11.3, Problem 30ES

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The factorization of the polynomial 12 x 2 + 28 x − 24 .

Solution Summary: The author calculates the factorization of the polynomial 12x2+28x-24 by foil method.

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