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 − 14 x + 2 x 2 as follows. Rewrite the expression as, 12 − 14 x + 2 x 2 = 2 ( x 2 − 7 x + 6 ) (1) Consider the expression x 2 − 7 x + 6 . It is observed that, the coefficients are a = 1 , b = − 7 and c = 6 . Step 1: Find the value of a c . Obtain the value of a c as, a c = 1 ( 6 ) = 6 Thus, the value of a c is 6. Step 2: Find the two number, e and f, whose product is a c = 6 and whose sum is b = − 7 . Obtain the list of integer factors of 6 such that the product is 6 and the sum is − 7 as shown below in Table 1. Integers whose product is 6 1 , 6 − 1 , − 6 2 , 3 − 2 , − 3 Sum 7 –7 5 –5 Table 1 From Table 1, it is observed that the numbers whose product is 6 and sum is –7 are − 1 and − 6 . Let the variables e = − 1 and f = − 6 . Step 3: Write a x 2 + b x + c = a x 2 + m x + n x + c

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 47E

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To factor: The expression 12−14x+2x2 completely.

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Chapter 6.2, Problem 46E

Chapter 6.2, Problem 48E

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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 expression 12 − 14 x + 2 x 2 completely.

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To factor: The expression 12−14x+2x2 completely.

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Chapter 6 Solutions