Question

Factor by grouping. $$ 2 x 3+2 x 2-x-1 $$

   Factor by grouping.
$$
2 x 3+2 x 2-x-1
$$

Elementary Algebra

Elementary Algebra

John Redden 1st Edition

Chapter 6, Problem 84

Instant Answer

Solved by Expert James Kiss

01/29/2022

Step 1

We group the terms with $x$ together and the constants together. So, the expression becomes: $$ 2x^3 - x + 2x^2 - 1 $$ Show more…

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Factor by grouping. $$ 2 x 3+2 x 2-x-1 $$

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Key Concepts

Common Factor Extraction

Common factor extraction is the initial step in many factoring techniques where you identify and remove the greatest common factor from a set of terms. This simplifies the expression and often prepares terms to be grouped or factored further using other techniques such as factor by grouping.

Factor by Grouping

Factor by grouping is a technique used for factoring polynomials that have four or more terms. It involves organizing the terms into groups such that each group has a common factor. Once each group is factored, any common binomial factors can be factored out, leading to a fully factored expression.

Polynomial Factoring

Polynomial factoring is the process of rewriting a polynomial as a product of two or more polynomials of lower degrees. This process simplifies solving equations, analyzing roots, and simplifying expressions by breaking down a complex expression into simpler multiplicative components.

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