Explanation Procedure used: Factoring general trinomials by grouping : In a trinomial of the form a x 2 + b x + c , a ≠ 1 , split up the x -term into two terms using the method described below. “Step 1: Find the product a c . Step 2: Find two numbers whose product is a c and whose sums is b . Step 3: Replace the middle term bx with two x -terms having these numbers as coefficients. That is, a x 2 + b x + c = a x 2 + m x + n x + c . Step 4: Complete the factorization by grouping”. Calculation: Factor the given expression 12 y 2 − 32 y − 12 as follows. Rewrite the expression 12 y 2 − 32 y − 12 . 12 y 2 − 32 y − 12 = 4 ( 3 y 2 − 8 y − 3 ) (1) Consider the expression 3 y 2 − 8 y − 3 . It is observed that, the coefficients are a = 3 , b = − 8 and c = − 3 . Step 1: Find the value of a c . Obtain the value of a c as, a c = 3 ( − 3 ) = − 9 Thus, the value of a c is − 9 . Step 2: Find the two number, m and n, whose product is a c = − 9 and whose sum is b = − 8 . Obtain the list of integer factors of − 9 such that product is − 9 and sum is − 8 as shown below in Table 1. Integers whose product is − 9 1 , − 9 − 1 , 9 − 3 , 3 Sum –8 8 0 Table 1 From Table 1, it is observed that the numbers whose product is − 9 and sum is − 8 are 1 and − 9 . Let, the variables m = − 9 and n = 1

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 6.2, Problem 21E

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To factor: The given expression 12y2−32y−12 completely.

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Chapter 6.2, Problem 20E

Chapter 6.2, Problem 22E

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Chapter 6 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

Ch. 6.1 - Prob. 1PE Ch. 6.1 - Prob. 2PE Ch. 6.1 - Prob. 3PE Ch. 6.1 - Prob. 4PE Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E

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To factor: The given expression 12 y 2 − 32 y − 12 completely.

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Chapter 6 Solutions