7.6 - Factoring by Grouping

Introduction:

This is a set of guiding questions and materials for creating your own lesson plan on factoring by grouping.

Common Core State Standards:

A.SSE.2

Learning Objectives:

To understand when to factor by grouping.
To learn how to factor by grouping.

Guiding Questions:

How do we factor a polynomial with more than three terms?

$2x^3-2x^2+3x-3$

In general, we don’t have a way of factoring polynomials of more than three terms, but what happens if we “group” terms that have a common factor and pull out that factor?
There seems to be more than one way to do this, how do we know which way to group?

Keep the goal (factoring) in mind.

$2x^2\left(x-1\right)+3\left(x-1\right)$ $2x^2\left(x-1\right)+3\left(x-1\right)$

How many terms do we have now?
What do those terms have in common, if anything?

$\left(x-1\right)\left(2x^2+3\right)$ $\left(x-1\right)\left(2x^2+3\right)$

Notes for Teachers:

If students have never been exposed to this factoring technique, it might take 10 to 15 minutes or more for them to explore and solve this problem. Don’t rush them. The time that a teacher spends on exploration will pay off in understanding. It will also make for a more efficient use of time since you won’t have to spend time repeating something that was not understood.

Video of the Day:

7.6.1 Factoring by Grouping

We demonstrate factoring by the grouping technique.

7.6.1 Factoring by Grouping.mp4 Download 7.6.1 Factoring by Grouping.mp4 Play media comment.

Exercises and Problems:

North Carolina Common Core Math 1 Item Bank, Nagy-Lup, p.19

Online Sources:

Khan Academy: Factoring by Grouping Applied to Quadratics Links to an external site.

Additional Resource for Teachers:

If you wish to download the contents of this page as a printable pdf, click here: 7.6 Factoring by Grouping.pdf Download 7.6 Factoring by Grouping.pdf