Factoring quadratics by grouping

Factoring by grouping

Learn about a factorization method called "grouping." For example, we can use grouping to write 2x²+8x+3x+12 as (2x+3)(x+4).

What you need to know for this lesson

Factoring a polynomial involves writing it as a product of two or more polynomials. It reverses the process of polynomial multiplication.

We have seen several examples of factoring already. However, for this article, you should be especially familiar with taking common factors using the distributive property. For example, 6x^2+4x=2x(3x+2)6x

2

+4x=2x(3x+2)6, x, squared, plus, 4, x, equals, 2, x, left parenthesis, 3, x, plus, 2, right parenthesis .

What you will learn in this lesson

In this article, we will learn how to use a factoring method called grouping.

Example 1: Factoring 2x^2+8x+3x+122x

2

+8x+3x+122, x, squared, plus, 8, x, plus, 3, x, plus, 12

First, notice that there is no factor common to all terms in 2x^2+8x+3x+122x

2

+8x+3x+122, x, squared, plus, 8, x, plus, 3, x, plus, 12. However, if we group the first two terms together and the last two terms together, each group has its own GCF, or greatest common factor:

In particular, there is a GCF of 2x2x2, x in the first grouping and a GCF of 333 in the second grouping. We can factor these out to obtain the following expression:

2x(x+4)+3(x+4)2x(x+4)+3(x+4)

Step-by-step explanation:

hopes it helps ^-^