Explanation Procedure used: Factoring a x 2 + b x + c , a ≠ 1 by grouping, where a, b and c have no common factors: “Step 1: Find the value of a c . Step 2: Find the pair of integers, m and n , whose product is a c and whose sums is b . Step 3: Write a x 2 + b x + c = a x 2 + m x + n x + c . Step 4: Factor the expression in step 3 by grouping. Step 5: Check by multiplying the factors.” Calculation: Obtain the factor of the polynomial as follows. Consider the given polynomial 6 y 2 − 17 y + 7 . It is observed that, there are no common factors and the coefficients are a = 6 , b = − 17 and c = 7 . Step 1: Find the value of a c . Obtain the value of a c as, a c = 6 ⋅ 7 = 42 Thus, the value of a c is 42 . Step 2: Find the pair of integers, m and n, whose product is a c = 30 and whose sum is b = − 17 . Obtain the list of integer factors of 42 such that product is 42 and sum is − 17 as shown below in Table 1. Integers whose product is 42 1 , 42 2 , 21 − 3 , − 14 6 , 7 14,3 Sum 42 23 − 17 13 21 Table 1 From the Table 1, it is observed that the integers whose product is 42 and sum − 17 is − 3 , − 14 . Let, the integers take the variables m = − 3 and n = − 14 . Step 3: Write a x 2 + b x + c = a x 2 + m x + n x + c . Rewrite the expression 6 y 2 − 17 y + 7 in the form a x 2 + m x + n x + c as, 6 y 2 − 17 y + 7 = 6 y 2 − 3 y − 14 y + 7 Step 4: Factor the expression in step 3 by grouping

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ISBN: 9780134556079

Author: Sullivan, Michael, III, Struve, Katherine R., Mazzarella, Janet.

Publisher: Pearson,

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Chapter 11, Problem 10CUR

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Chapter 11 Solutions

Elementary & Intermediate Algebra

Ch. 11.1 - Given two functions f and g, the ____ ____,...Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E Ch. 11.1 - Prob. 9E Ch. 11.1 - Prob. 10E

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The factor of the polynomial 6 y 2 − 17 y + 7 .

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