Explanation Procedure used: Factoring a x 2 + b x + c , a ≠ 1 using trial and error: Step 1: If there are common factors, then factor out the GCF and obtain the trinomial. Step 2: List the possibilities for the first terms of each binomial whose product is a x 2 . Step 2: List the possibilities for the last terms of each binomial. Step 3: Write all the combinations of factors found in step 1 and step 2. Multiply the binomials until a product that equals the trinomial is found.” Step 6: Check whether the factors satisfies the given polynomial or not. Calculation: The given polynomial is 8 m 2 + 18 m + 9 . It is noted that, there are no common factors. There are two possibilities for the first term 8 m 2 of the trinomial that is, ( m + _ ) ( 8 m + _ ) and ( 2 m + _ ) ( 4 m + _ ) . List the possibilities for the last terms of each binomial factor whose product should be 9 as shown below in Table 1. Factors of 9 : 1 , 9 3 , 3 − 1 , − 9 − 3 , − 3 Table 1 Since the coefficient of the middle term 18 is positive, the integer pair for the second term of the binomial factor is chosen as follows. The addition of outer and inner product that results in a positive value is considered that is, 1 , 9 and 3 , 3 . When the integer pairs 1 , 9 and 3 , 3 are substituted in the binomial pair ( m + _ ) ( 8 m + _ ) , the sum of the outer and inner product results in a larger value when compared with 18 m . Hence, the possibility of the factor ( m + _ ) ( 8 m + _ ) is not considered

3rd Edition

ISBN: 9780321880116

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

Publisher: PEARSON

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Chapter 6, Problem 40RE

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To factorize: The polynomial 8m2+18m+9 completely and if it could not be factored state that it is prime.

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Chapter 6, Problem 39RE

Chapter 6, Problem 41RE

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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 factorize: The polynomial 8 m 2 + 18 m + 9 completely and if it could not be factored state that it is prime.

Solution Summary: The author explains how to factorize the polynomial 8m2+18m+9 using trial and error.

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To factorize: The polynomial 8m2+18m+9 completely and if it could not be factored state that it is prime.

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Chapter 6 Solutions