Explanation Procedure used: “Factoring trinomial of the Form x 2 + b x + c : Step 1: Find the pair of integers whose product is c and whose sum is b . That is, determine m and n such that m n = c and m + n = b . Step 2: Write x 2 + b x + c = ( x + m ) ( x + n ) . Step 3: Check your work by multiplying the binomials”. Calculation: Consider the trinomial m 2 n 2 − 8 m n + 12 . The trinomial can be written as ( m n ) 2 − 8 ( m n ) + 12 . The trinomial ( m n ) 2 − 8 ( m n ) + 12 is in the form of ( m n ) 2 + b m n + c , where b = − 8 and c = 12 . Find the pair of integers whose product is 12 and sum is –8. Notice that, if the coefficient of the middle term is negative and the constant is positive, then both the factors of the constant must be negative. List all factors of 12 where the factors are negative and obtaining the sum of those factors. Factors of 12 –1, –12 –2, –6 –3, –4 Sum –13 –8 –7 Choose m = − 6 and n = − 2 because the product m n = 12 and the sum m + n = − 8

3rd Edition

ISBN: 9780321880116

Author: Michael Sullivan III, Katherine R. Struve, Janet Mazzarella

Publisher: PEARSON

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Chapter 6.2, Problem 83E

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To factor: The trinomial m2n2−8mn+12.

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Chapter 6.2, Problem 82E

Chapter 6.2, Problem 84E

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Chapter 6 Solutions

Elementary & Intermediate Algebra

Ch. 6.1 - The largest polynomial that divides evenly into a...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 Ch. 6.1 - Prob. 7E Ch. 6.1 - Prob. 8E Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E

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To factor: The trinomial m 2 n 2 − 8 m n + 12 .

Solution Summary: The author explains how to factor a trinomial in the form x2+bx+c.

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To factor: The trinomial m2n2−8mn+12.

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Chapter 6 Solutions