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

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ISBN: 9780321997173

Author: Marvin L. Bittinger, Judith A. Beecher

Publisher: PEARSON

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Chapter 11.3, Problem 6DE

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The factorization of the polynomial 2 − x − 6 x 2 .

Solution Summary: The author calculates the factorization of the polynomial 2-x-6x2 by foil method.

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