Common Factoring

Common Factoring means to find the greatest common factor of all the terms in the algebraic expression. This factor can be a number, a variable, or both.

What you want to do first is consider the numbers and variables making up each term.

Then you want to write the common factor in front of the brackets. In the brackets, you would write the algebraic expression resulting from dividing EACH term by the common factor.

Let’s try an example:

Factor the following: 16xy^2 + 20x^2y – 4x^3y^2

First look at the coefficients (numbers) and write their GCF. For our equation the GCF of 16, 20, and 4 is 4 since…

16 ÷ 4 = 4

20 ÷ 4 = 5

4 ÷ 4 = 1

It divides into all the numbers evenly.

Now we look at the variables and write their GCF. For our equation the GCF of xy^2, x^2y, and x^3y^2 is xy because…

xy^2 ÷ xy = y

x^2 y ÷ xy = x

x^3 y^2 ÷ xy = x^2y

It divides into all the variables evenly.

Therefore the GCF of this equation is 4xy.

So now what you want to do is divide all the terms in the equation by 4xy.

16xy^2/4xy + 20x^2y/4xy – 4x^3y^2/4xy

= 4xy (4y + 5x – x^2y)

**you can check you answer by expanding the equation. The answer should be the original expression.**

4xy(4y + 5x – x^2y)

= 4xy(4y) + 4xy(5x) + 4xy(–x^2y)

= 16xy^2 + 20x^2y – 4x^3y^2

Now you try…

Factor the following: –144p^5q – 12p^3 −6p

Answer…

= −6p (24p^4q + 2p^2 + 1)

Extra Practice…

A Video for Extra Help...