Factoring Polynomial Worksheets

Factoring Polynomial Worksheets

Factoring Polynomial worksheets is a method to split algebraic expressions into factors that can be multiplied. These factoring polynomial worksheets give students additional practice on working with polynomials.  Included factoring polynomial worksheets to factorized linear expressions, monomials, quadratic expressions, and polynomials and binomials using a wide range of processes, such as Grouping, synthetic division, and box method. These factoring polynomial worksheets with answer keys offer students immense practice.

Factoring Polynomial Worksheets
Factoring Polynomial Worksheets

Below stated factoring polynomial worksheets will help students progress toward becoming an algebraic expert, and they will learn to factor polynomials in a variety of ways. Students can use the FOIL algorithm to make links between polynomials and factored expressions, or for more tactile learning, teachers can show their class how to construct each equivalent expression using algebraic tiles.

Factoring Polynomial Worksheets with answers
Factoring Polynomial Worksheets with answers

In this article, we will investigate different approaches using some examples to factoring polynomial worksheets.

Factoring Quadratics Worksheets

This factoring polynomials worksheet will produce problems for factoring quadratics expressions. Students can select which type of polynomials to factor, and whether they want some non-factorable expressions or not. This type of sheet include;

Factoring Polynomial Worksheets printable
Factoring Polynomial Worksheets printable
  • Type of quadratic polynomials to factor
    • Binomials
    • Trinomials
    • Mixture of both
  • Some non-factorable polynomials
    • Non-factorable polynomials
    • Not non-factorable polynomials
  • Coefficient of first term (a=?)
    • The first term equal to (a=1)
    • The first term greater than 1 (a>1)
    • Mixture of both
      Factoring Polynomial Worksheets pdf
      Factoring Polynomial Worksheets pdf

Factoring polynomial worksheet by Grouping

The very first thing we will do when factoring is trying to factor out a GCF. This GCF is a monomial like 5xy+10xz; the GCF is monomial 5x so that we would have 5x(y+2z). A GCF doesn’t have to be a monomial, it could be a binomial. For example:

Factoring Polynomial Worksheets kuta
Factoring Polynomial sheet kuta
  • 3ax-7bx (both have x in common so that we will factor it out)
  • x(3a-7b) is our solution

Another example that has (2a+5b) instead of x.

  • 3a(2a+5b)-7b(2a+5b) (both have 2a+5b in common, so that we will factor it out)
  • (2a+5b)(3a-7b) is our solution

In the same process, we factored out a GCF of x we can factor out a GCF, which is a binomial, 2a+5b. This factoring polynomial worksheet can be stretched to factor problems where there is no GCF to factor out, or after the GCF is factored out, there is some factoring that can be done. We will use another way to factor. We can use a process which is called Grouping.

Factoring Polynomial Worksheets free online
Factoring Polynomial method free online

Factoring polynomial worksheets Grouping

Grouping is how we will factor if there are four terms in the problem. Factoring is like multiplying in reverse, so the first thing we will do is to look at a multiplication process and then try to reverse the method.

download Factoring Polynomial Worksheets
download Factoring Polynomial sheet

For example;

  • (2a+3b)(5b+2) Distributing 2a+3 into the second parenthesis
  • 5b(2a+3)+2(2a+3) Distributing each monomial
  • 10ab+15b+4a+6 Our solution


The key for Grouping to work is after the GCF is factored out of the left and right; the two binomials must match exactly. If the two binomials are not matching, we either have to make some adjustments or it cant be factored using the grouping method.