Explanation Given Information: The provided polynomial is − 19 x + 15 x 2 + 6 . 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, − 19 x + 15 x 2 + 6 Rewrite the polynomial in descending order, 15 x 2 − 19 x + 6 Take the combination of two terms, whose product is 15 x 2 , Combination of terms Product 3 x and 5 x 15 x 2 15 x and x 15 x 2 Write this combination in factor form, as, ( 3 x + ) ( 5 x + ) or ( 15 x + ) ( x + ) Take the possible pairs of two terms, whose product is 6 , Possible pairs Product of pairs 2 , 3 6 3 , 2 6 6 , 1 6 1 , 6 6 − 2 , − 3 6 − 3 , − 2 6 − 6 , − 1 6 − 1 , − 6 6 Here the sign of the middle term is negative and the sign of the last term is positive. So, select the negative pairs to keep the sign of the terms unchanged. Form the pair to get middle term − 19 by checking each possible pair via substituting the combination in the factor form, as, Trial Product Remark ( 3 x − 2 ) ( 5 x − 3 ) 15 x 2 − 9 x − 10 x + 6 = 15 x 2 − 19 x + 6 Middle term is − 19 , 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 42ES

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The factorization of the polynomial − 19 x + 15 x 2 + 6 .

Solution Summary: The author calculates the factorization of the polynomial -19x+15x2+6 by foil method.

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