Explanation Given Information: The polynomial is 6 t 3 + 9 t 2 − 15 t . Formula used: Steps for factorization a trinomial by a c -Method are: Step 1: Factor out the greatest common factor, if any. Write the resultant trinomial as a x 2 + b x + c . Step 2: Multiply the coefficient of x 2 and the constant term c . Step 3: Determine p and q , the factors of the product a c , such that p q = a c and p + q = b . Step 4: Write the middle term, b, as the sum of the factors obtained in step (3). Step 4: Factor the expression be grouping. Step 5: Check the result by multiplying the factors obtained in step (4). Calculation: Consider the provided expression 6 t 3 + 9 t 2 − 15 t . Factor out the common factor 3 t from the provided polynomial as follows: 6 t 3 + 9 t 2 − 15 t = 3 t ( 2 t 2 + 3 t − 5 ) Factorize the polynomial 2 t 2 + 3 t − 5 using the a c -Method as follows: Multiply the coefficient of t 2 , 2 and the constant term − 5 , 2 × ( − 5 ) = − 10 Since, the coefficient of t is positive and product of coefficient of x 2 and constant term is negative. So, select a positive and a negative factor of − 10 . Thus, the positive and negative factor of − 10 and their sum is as follows: Pairs of factors Sum of factors ( − 1 ) × ( 10 ) − 1 + ( 10 ) = 9 ( − 2 ) × ( 5 ) − 2 + ( 5 ) = 3 Now arrange the factors of − 10 in a way that their sum will give the coefficient of t that is 3 in the polynomial 2 t 2 + 3 t − 5 . The product of − 2 and 5 is − 10 and the sum of − 2 + ( 5 ) is 3

9th Edition

ISBN: 9780321997173

Author: Marvin L. Bittinger, Judith A. Beecher

Publisher: PEARSON

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Chapter 11, Problem 19T

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To calculate: The factorization of the polynomial 6t3+9t2−15t.

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Chapter 11, Problem 18T

Chapter 11, Problem 20T

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Chapter 11 Solutions

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The factorization of the polynomial 6 t 3 + 9 t 2 − 15 t .

Solution Summary: The author calculates the factorization of the polynomial 6t3+9

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To calculate: The factorization of the polynomial 6t3+9t2−15t.

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Chapter 11 Solutions