Factoring Expressions (By Grouping)

Related Topics:
Common Core (Algebra)
Common Core for Mathematics

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

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

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

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

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

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

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