Factoring Expressions (By Grouping)

Examples, solutions, videos, and lessons to help High School students learn to use the structure of an expression to identify ways to rewrite it. For example, see x⁴ – y⁴ as (x²)² – (y²)², thus recognizing it as a difference of squares that can be factored as (x² – y²)(x² + y²).

Suggested Learning Targets

• Use factoring techniques such as common factors, grouping, the difference of two squares, the sum or difference of two cubes, or a combination of methods to factor completely.
• Simplify expressions including combining like terms, using the distributive property and other operations with polynomials.

Common Core: HSA-SSE.A.2

The following diagram shows a factoring technique called factor by grouping. Scroll down the page for more examples and solutions.

 

Factor by Grouping

Factor by Grouping and Factoring Completely.
Factor 4x² + 25x - 21
Factor 6x² + 7x + 1
Factor -x³ + 17x² - 70x

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Factoring Trinomials: Factor by Grouping - ex 1.
Factor 12x² + 34x + 10

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Factoring Trinomials: Factor by Grouping - ex 2.
Factor 6x² + 15x - 2

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Factoring Trinomials: Factor by Grouping - ex 3.
Factor - 8x² + 60x - 28

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Factoring by Grouping (4 terms) - Ex 1.
a) 2x³ + 7x² + 2x + 7
b) 10x² + 2xy + 15xy + 3y²

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Factoring by Grouping (4 terms) - Ex 2.
12x² + 15uv + 24uv² + 30v³

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