Factoring Expressions (By Grouping)

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

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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.

Factoring by Grouping

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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