Explanation Procedure used: Factoring a Polynomial Using the Greatest Common Factor: “Step 1: Identify the greatest common factor (GCF) of the terms of the polynomial. Step 2: Rewrite each term as the product of the GCF and the remaining factor. Step 3: Use the Distributive Property “in reverse” to factor out the GCF. Step 4: Check using the Distributive Property”. Calculation: The given polynomial is 14 m 2 − 16 m 3 − 24 m 4 . In order to factor the polynomial 14 m 2 − 16 m 3 − 24 m 4 , first compute the GCF of the terms of the polynomial. The terms of the polynomial 14 m 2 − 16 m 3 − 24 m 4 can be written as the product of prime factors as follows. 14 m 2 = − 2 ⋅ − 7 ⋅ m ⋅ m − 16 m 3 = − 2 ⋅ 8 ⋅ m ⋅ m ⋅ m − 24 m 4 = − 2 ⋅ − 2 ⋅ − 2 ⋅ 3 ⋅ m ⋅ m ⋅ m ⋅ m Note that, the coefficients, 14, –16 and –24 in the polynomial 14 m 2 − 16 m 3 − 24 m 4 has the common factors –2 and the monomials m 2 , m 3 and m 4 has the product of two factors of m in common. That is, the GCF of the terms of the polynomial is − 2 m 2 . Now rewrite the terms 14 m 2 , − 16 m 3 and − 24 m 4 as the product of the GCF and the remaining factor then factor out the GCF as below

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ISBN: 9780321880116

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

Publisher: PEARSON

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Chapter 6.1, Problem 62E

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To find: The factor of the polynomial 14m2−16m3−24m4 by factoring out the GCF.

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Chapter 6.1, Problem 61E

Chapter 6.1, Problem 63E

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The factor of the polynomial 14 m 2 − 16 m 3 − 24 m 4 by factoring out the GCF.

Solution Summary: The author explains how to factor a polynomial using the greatest common factor (GCF) and the Distributive Property (in reverse).

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To find: The factor of the polynomial 14m2−16m3−24m4 by factoring out the GCF.

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