Explanation Procedure used: Step 1: To check whether the given polynomial has a greatest common factor. Step 2: Count the number of terms in the polynomial inside parentheses. Step 3: Frame the polynomial in form of ( x + m ) ( x + n ) , where m n = c and m + n = b . Step 4: Multiply the obtained factors to check the correctness. Calculation: The given polynomial is x 3 − x 2 − 42 x . The polynomial can be written as x ( x 2 − x − 42 ) . By the above procedure, the greatest common factor of x 3 − x 2 − 42 x is x and has 3 terms that is trinomial. Compare the trinomial x 2 − x − 42 with a x 2 + b x + c to get the values of a , b and c . That is, a = 1 , b = − 1 and c = − 42 . Obtain the product of m and n . m n = a c = ( 1 ) ( − 42 ) = − 42 Find the two integers whose product is –42 and whose sum is –1. The product is ( 6 ) ( − 7 ) = − 42 and the sum is 6 + ( − 7 ) = − 1 . Then the required integers are m = 6 and n = − 7 . Now factorize x 3 − x 2 − 42 x in the form of ( x + m ) ( x + n ) as follows

3rd Edition

ISBN: 9780321880116

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

Publisher: PEARSON

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Chapter 6, Problem 67RE

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To factorize: The polynomial x3−x2−42x.

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Chapter 6, Problem 66RE

Chapter 6, Problem 68RE

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Chapter 6 Solutions

Elementary & Intermediate Algebra

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To factorize: The polynomial x 3 − x 2 − 42 x .

Solution Summary: The author explains how to factorize a given polynomial, which is x3-242x, by calculating its greatest common factor.

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To factorize: The polynomial x3−x2−42x.

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