Question

Factor each polynomial. $$ 4 a^{2} b^{2} c-6 a b^{2} c-4 a c+8 a $$

   Factor each polynomial.
$$
4 a^{2} b^{2} c-6 a b^{2} c-4 a c+8 a
$$

Intermediate Algebra

Intermediate Algebra

Elayn Martin-Gay 6th Edition

Chapter 5, Problem 48

Instant Answer

Solved by Expert James Kiss

07/18/2020

Step 1

In this case, the GCF is $2a$. Show more…

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Factor each polynomial. $$ 4 a^{2} b^{2} c-6 a b^{2} c-4 a c+8 a $$

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Key Concepts

Common Factoring

This concept involves identifying and extracting the greatest common factor (GCF) shared by all terms in a polynomial. Recognizing the largest expression that divides each term simplifies the polynomial and can reveal further structure such as factorable groups or binomials.

Factoring by Grouping

This method is useful when a polynomial does not have a single common factor among all terms but can be separated into groups that share common factors. By grouping terms appropriately and factoring each group individually, one can often factor the polynomial completely.

Distributive Property

The distributive property underlies the process of factoring and expanding expressions. It allows one to factor out common terms or combine like terms by showing that a product over a sum (or difference) can be rewritten as a sum (or difference) of products.

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