Factoring Out a GCF – Solve and Match Worksheet

Greatest common factors are pulled out of eighteen polynomial expressions, nine in x alone and nine in a and b, with the remaining factor matched to a lettered bank and the whole set worked out on the marked pages.

Grades: Grades 9–12
File type: PDF
Preparation: Print ready

Updated Mar 01, 2023

Subject: Algebra, Math
Topic: Solve and Match, Factoring
Resource types: Worksheets, Worksheets & Printables
Preparation: Print ready

From the author

About this resource

This Solve & Match worksheet allows students to practice factoring out a greatest common factor (GCF) from an algebraic expression. There are eighteen problems in total. Some expressions have multiple variables, some expressions just use one variable. Once students factor out the GCF, they need to find the resulting factor in the answer bank and match the answer letter with the problem number.

Solve & Match worksheets help students build confidence in their skills when they are able to find their answer in the answer bank! It also alleviates students constantly asking the teacher if their answer is correct. Each answer in the answer bank will only be used once!

This worksheet is suitable for students who are just learning how to factor our a GCF. It works great as an in-class assignment or as a homework assignment!

Access To Resource:

This is a Google Drive Activity. Both the teacher and student must have a Google account in order to use this resource. When you open up the file you will click on the link which will prompt you to create a copy. The copy will then be saved to your Google Drive and you can assign the activity accordingly to your students.

Other Skills Offered As Solve & Match Worksheets:

-Calculating Slope

-Exponential Equations with a Common Base

-Exponential Equations without a Common Base

-Factoring by Grouping

-Factoring Out a GCF

-Factoring Polynomials

-Factoring Trinomials (a is greater than 1)

-Factoring Trinomials (a is equal to 1)

-Laws of Exponents (Positive and Negative)

-Laws of Exponents (Positive Only)

-Solving Logarithmic Equations

-Solving Polynomial Equations

-Solving Quadratic Equations

-Solving Radical Equations

-Solving Rational Equations

-Simplifying Expressions

-Solving Linear Equations

-Solving Two-Step Equations

In the classroom

Teaching tips & learning objectives

Learning objectives

Identify the greatest numerical factor shared by every term of a polynomial
Identify the lowest power of each variable present in all terms and include it in the common factor
Write an expression as the product of its greatest common factor and the remaining polynomial
Handle two-variable expressions where the common factor combines a coefficient with powers of both letters
Use the one-letter-per-problem constraint to check a block of nine before handing it in

Teaching tips

Problems 1 to 9 build the idea one variable at a time; hold back the a and b block until the class is reliably taking out both the number and the power of x
Problem 5, 4x³ + x, is the one students most often leave alone, because the common factor is just x and the second term looks like it has nothing to give — worth working together
Ask for the factored form written out in full even though only the letter goes in the box; the letter alone hides whether the numerical factor was taken as far as it goes
The bank prints only the second factor, so a student who takes out 4x instead of 2x will not find their answer — that failure is the point, and is worth naming before they start
The same activity exists as a Google Slides version accessed from the first page, so a class working on devices and a class working on paper can be set the same eighteen problems

Skills covered

Factoring out a numerical GCF — problems such as 10x + 2 and 18x − 15 ask for the number common to both terms before any variable work begins.
Factoring out a variable GCF — 2x² + 7x, 3x³ − 4x² and 4x³ + x require the lowest power of x present in every term to come out with it.
Combining numerical and variable factors — 18x² + 4x, 8x³ − 12x² + 4x and 10x⁴ − 8x³ + 6x² need a coefficient and a power of x taken together.
Working in two variables — problems 10 to 18 use terms in a and b, so the common factor takes the lowest power of each letter along with the numerical factor.
Self-checking through the letter bank — nine lettered factors serve nine problems in each block and each is used once, so an unmatched answer sends the student back to the expression.

Good to know

Questions teachers ask about this resource

How do the two blocks of problems differ?

Problems 1 to 9 are single-variable expressions in x, where the common factor is a number, a power of x, or both. Problems 10 to 18 use two variables and heavier coefficients — 48a³b + 84a²b², 72a⁴b³ − 40a³b⁴ + 24a³b³ — so the factor taken out combines a number with powers of both a and b.

What exactly goes in the box under each problem?

A single letter. Students factor the expression, look for the polynomial factor that remains in the bank printed on that page, and write its letter in the box. For problem 2, 18x − 15 factors to 3(6x − 5), and (6x − 5) is listed as G.

What is on the first page of the file?

An access page for the digital version, directing the user to a link that opens the same activity in Google Slides and stating that the marked pages follow it. The printable worksheet and its worked pages make up the rest of the file.