Introduction
Factoring is an important skill that math students need to understand. It’s a foundation to solving equations, simplifying expressions, and graphing functions. There are multiple methods to factoring a polynomial, but here we will focus on factoring using a GCF (Greatest Common Factor).
When factoring a polynomial, the objective is to change the sum and difference of many terms into the product of different polynomials. For example, if one were asked to factor the number 12, one might write 2*2*3, because these are the smallest numbers that multiply to make 12.
It is important that we be able to do this with polynomials as well. Breaking them down into the product of smaller pieces (factors) allows us to simplify problems.
When choosing to factor a polynomial, start by determining if there is a Greatest Common Factor (GCF), which is a monomial (1- term) that divides evenly into each term of the polynomial.
Example
Given:
4x2y3 − 6xy2 + 2x3y4
We can determine that the GCF they all have in common is 2xy2 We will divide each term by this monomial.
2xy − 3y + xy2
When you divide each term by the GCF (also known as factoring out the GCF), you will get 2xy – 3 + xy2
When writing the result, the GCF is placed in front of a set of parentheses and the rest is left inside the parentheses as follows:
2xy2(2xy - 3y + xy2)
To confirm you did it correctly, verify:
- The polynomial inside the parentheses no longer has something in common. This illustrates you chose the GREATEST common factor
- Re-distribute your GCF through the parentheses to verify you can get the original question back again, confirming you didn’t make any computational errors
Practice Problems: Now you try!
- 2x2 + 8x
- 8x–12
- 5x3y+x2
- 12x2–9x+21
- –4a2b3–6a4b2–18a3b5
- 7x2–30
For more guides on math topics, visit the Academic Support Module in Brightspace and search Resources, or visit our YouTube Channel “All Math Videos” playlist.
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