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 6 x 2 + x − 5 as follows. It is observed that, the coefficients are a = 6 , b = 1 and c = − 5 . Step 1: Find the value of a c . Obtain the value of a c as, a c = 6 ( − 5 ) = − 30 Thus, the value of a c is –30. Step 2: Find the two number, m and n, whose product is a c = − 30 and whose sum is b = 1 . Obtain the list of integer factors of − 30 such that product is − 30 and sum is 1 as shown below in Table 1. Integers whose product is − 30 1 , − 30 15 , − 2 − 15 , 2 6 , − 5 − 6 , 5 Sum –29 13 –13 1 –1 Table 1 From Table 1, it is observed that the numbers whose product is − 30 and sum is 1 are − 5 and 6

Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus

11th Edition

ISBN: 9780134434636

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 6.2, Problem 31E

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To factor: The given expression 6x2+x−5 completely.

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Chapter 6.2, Problem 30E

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Chapter 6 Solutions

Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus

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 6 x 2 + x − 5 completely.

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Chapter 6 Solutions