Explanation Procedure used: Factoring a x 2 + b x + c , a ≠ 1 by grouping, where a, band c have no common factors: “Step 1: Find the value of a c . Step 2: Find the pair of integers, m and n , whose product is a c and whose sums is b . Step 3: Write a x 2 + b x + c = a x 2 + m x + n x + c . Step 4: Factor the expression in step 3 by grouping. Step 5: Check by multiplying the factors.” Calculation: Obtain the factor of the trinomial as follows. Consider the given trinomial 6 m 2 − m − 5 . For the trinomial 6 m 2 − m − 5 , the values of the coefficients are a = 6 , b = − 1 and c = − 5 where a c is the product and b is the sum. Find the value of a c . a c = 6 ( − 5 ) = − 30 Thus, the value of the product is a c = − 30 . Since the product is –30 and the sum is –1, one factor must be negative and the other should be positive. Note that the sum of the numbers is negative, therefore the larger integer factor must be negative. Obtain the list of integer factors of –30 as shown below in Table 1. Integers whose product is –30 1, –30 2, –15 3, –10 5, –6 Sum –29 –13 –7 –1 Table 1 From Table 1, it is observed that the integers whose product is –30 and sum is –1 are 5 and − 6 . Let, the pair of integers m and n take the values, m = − 6 and n = 5 . Rewrite the expression 6 m 2 − m − 5 in the form a x 2 + m x + n x + c as, 6 m 2 − m − 5 = 6 m 2 − 6 m + 5 m − 5 Factor the above expression by grouping as follows

3rd Edition

ISBN: 9780321880116

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

Publisher: PEARSON

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Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.

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Chapter 6, Problem 7T

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To factor: The trinomial 6m2−m−5 and state that the trinomial is prime, if it cannot be factored.

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Chapter 6, Problem 6T

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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 6 m 2 − m − 5 and state that the trinomial is prime, if it cannot be factored.

Solution Summary: The author states that the trinomial 6m2-m-5 is prime, if it cannot be factored.

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To factor: The trinomial 6m2−m−5 and state that the trinomial is prime, if it cannot be factored.

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Chapter 6 Solutions