Explanation Given information: The polynomial is 15 − 8 x + x 2 . Formula used: Steps for factorization a trinomial by a c -Method are: Step 1: Factor out the greatest common factor, if any. Write the resultant trinomial as a x 2 + b x + c . Step 2: Multiply the coefficient of x 2 and the constant term c . Step 3: Determine p and q , the factors of the product a c , such that p q = a c and p + q = b . Step 4: Write the middle term, b, as the sum of the factors obtained in step (3). Step 4: Factor the expression be grouping. Step 5: Check the result by multiplying the factors obtained in step (4). Calculation: Consider the provided expression 15 − 8 x + x 2 . Arrange the polynomial in descending power of x as follows: 15 − 8 x + x 2 = x 2 − 8 x + 15 Factorize the polynomial x 2 − 8 x + 15 using the a c -Method as follows: Multiply the coefficient of x 2 , 1 and the constant term 15 , 1 × ( 15 ) = 15 Since, the coefficient of x is negative and product of coefficient of x 2 and constant term is positive. So, select a negative factor of 15 . Thus, the possible positive and negative factors of 15 and their sum is as follows: Pairs of factors Sum of factors − 1 × ( − 15 ) − 1 + ( − 15 ) = − 16 − 3 × ( − 5 ) − 3 + ( − 5 ) = − 8 Now arrange the factors of 15 in a way that their sum will give the coefficient of x that is − 8 in the polynomial x 2 − 8 x + 15 . The product of − 3 and − 5 is 15 and the sum of − 3 + ( − 5 ) is − 8

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ISBN: 9780321997173

Author: Marvin L. Bittinger, Judith A. Beecher

Publisher: PEARSON

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Chapter 11, Problem 27RE

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Chapter 11 Solutions

Developmental Mathematics (9th Edition)

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The factorization of the polynomial 15 − 8 x + x 2 .

Solution Summary: The author calculates the factorization of the polynomial 15-8x+x2 using the ac-Method.

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Chapter 11 Solutions