Factoring Expressions Worksheets
Free printable worksheets on factoring linear expressions. Take out the greatest common factor: 8x + 12 = 4(2x + 3). Answer key included.
Each question is a two-term expression to factor: 8x + 12 = ____(________). Find the greatest number that divides both terms - here 4 - write it in front of the bracket, and put what is left inside: 4(2x + 3).
The two terms always share a factor from 2 to 9, and the key takes out the greatest one, so nothing inside the bracket has a common factor left. 2(4x + 6) equals 8x + 12 but is not finished: 4x and 6 still share a 2. No number on the sheet is larger than 12.
What this worksheet covers
- Find the greatest common factor of the terms in an expression
- Factor an expression by taking out the greatest common factor
Common Core standards
- 6.EE.A.3 Apply the properties of operations to generate equivalent expressions.
- 7.EE.A.1 Apply properties of operations as strategies to add, subtract, factor and expand linear expressions.
Frequently asked questions
How do you factor an expression?
Find the greatest common factor of the terms, write it in front of a bracket, and divide each term by it. For 6x + 9 the greatest common factor is 3, and 6x ÷ 3 = 2x and 9 ÷ 3 = 3, so the answer is 3(2x + 3).
How do I check a factored answer?
Multiply it back out. 3(2x + 3) expands to 6x + 9, which is where it started. Factoring and the distributive property are the same step run in opposite directions.
Is 2(4x + 6) wrong?
It is equal to 8x + 12, but it is not fully factored: 4x and 6 still have a common factor of 2. The key always takes out the greatest common factor, which leaves nothing more to take out.
What grade is this?
Sixth grade introduces it alongside the distributive property, and seventh grade names factoring as a skill of its own. The first term on this page is always positive, so the factor in front is never negative.