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 m 2 + 60 m + 75 as follows. Rewrite the expression 12 m 2 + 60 m + 75 as, 12 m 2 + 60 m + 75 = 3 ( 4 m 2 + 20 m + 25 ) (1) Consider the expression 4 m 2 + 20 m + 25 . It is observed that, the coefficients are a = 4 , b = 20 and c = 25 . Step 1: Find the value of a c . Obtain the value of a c as, a c = 4 ( 25 ) = 100 Thus, the value of a c is 100. Step 2: Find the two number, e and f, whose product is a c = 100 and whose sum is b = 20 . Obtain the list of integer factors of 100 such that product is 100 and sum is 20 as shown below in Table 1. Integers whose product is 100 1 , 100 − 100 , − 1 − 10 , − 10 10 , 10 50 , 2 Sum 101 –101 –20 20 52 Table 1 From Table 1, it is observed that the numbers whose product is 100 and sum is 20 are 10 and 10 . Let, the variables e = 10 and f = 10 . 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 35E

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To factor: The given expression 12m2+60m+75 completely.

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Chapter 6.2, Problem 34E

Chapter 6.2, Problem 36E

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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 m 2 + 60 m + 75 completely.

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