Explanation Procedure used: “Factoring trinomial of the form x 2 + b x y + c y 2 : 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 y + c y 2 = ( x + m y ) ( x + n y ) . Step 3: Check your work by multiplying the binomials”. Calculation: Consider the trinomial r 2 + r s − 6 s 2 . The trinomial r 2 + r s − 6 s 2 is in the form of r 2 + b r s + c s 2 , where b = 1 and c = − 6 . Find the pair of integers whose product is –6 and sum is 1. Note that, the value of c is negative, so one of the factors must be positive and another one is negative and the value of b is odd, and the factor with the larger absolute value is positive. List all factors of –6 where the factors are negative and obtaining the sum of those factors. Factors of –6 –1, 6 –2, 3 Sum 5 1 Choose m = 3 and n = − 2 because the product m n = − 6 and the sum m + n = 1

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ISBN: 9780321880116

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

Publisher: PEARSON

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Chapter 6.2, Problem 39E

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To factor: The trinomial r2+rs−6s2 and state that the trinomial is prime, if it cannot be factored.

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Chapter 6.2, Problem 38E

Chapter 6.2, Problem 40E

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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 r 2 + r s − 6 s 2 and state that the trinomial is prime, if it cannot be factored.

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To factor: The trinomial r2+rs−6s2 and state that the trinomial is prime, if it cannot be factored.

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Chapter 6 Solutions