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 y 2 − 33 y − 18 as follows. Rewrite the expression as, 6 y 2 − 33 y − 18 = 3 ( 2 y 2 − 11 y − 6 ) (1) Consider the expression 2 y 2 − 11 y − 6 . It is observed that, the coefficients are a = 2 , b = − 11 and c = − 6 . Step 1: Find the value of a c . Obtain the value of a c as, a c = 2 ( − 6 ) = − 12 Thus, the value of a c is –12. Step 2: Find the two number, e and f, whose product is a c = − 12 and whose sum is b = − 11 . Obtain the list of integer factors of –12 such that the product is –12 and the sum is − 11 as shown below in Table 1. Integers whose product is –12 1 , − 12 − 1 , 12 6 , − 2 − 6 , 2 Sum –11 11 4 –4 Table 1 From Table 1, it is observed that the numbers whose product is –12 and sum is –11 are 1 and − 12 . Let the variables e = 1 and f = − 12 . Step 3: Write a x 2 + b x + c = a x 2 + m x + n x + c

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 48E

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To factor: The expression 6y2−33y−18 completely.

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Chapter 6.2, Problem 47E

Chapter 6.2, Problem 49E

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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 expression 6 y 2 − 33 y − 18 completely.

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To factor: The expression 6y2−33y−18 completely.

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Chapter 6 Solutions