A. Further Review of Factoring

In Lesson 2.2 you reviewed greatest common factors (GCF) and how to factor trinomials of the form when . As you learn how to solve quadratic equations throughout this Lesson, you may find a review of the following factoring techniques helpful.

Factoring strategy When to use it Example
Greatest Common Factors (GCFs) Any polynomial can be checked for common factors.

Eg 1.

Eg 2.

Trinomial when a = 1 Used for trinomials of the form

Eg 1.

Find two values that sum to −1 and have a product of −20.

−5 + 4 = −1 and −5 × 4 = −20

Write the trinomial as a product of its factors.
Trinomial when Used for trinomials of the form

Eg. 1.

Find two values that have a product of 24 and sum to 11.

8 × 3 = 24 and 8 + 3 = 11

Decompose the middle term, group, and factor.
Difference of squares Used for polynomials of the form

Eg 1.

Check by Expanding

Eg 2.

First term in each factor:

Last term in each factor: