7th grade factoring out a specified rational factor worksheets

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Each of these eight expressions comes with a nonzero rational factor. Students divide both terms by that factor and write the expression as a product, then expand to check. Easier uses mostly positive proper fractions and smaller integer quotients. On level balances positive and negative factors with varied signs inside the parentheses. Harder uses more negative and improper factors, so students must coordinate signs carefully.

Free printable PDF worksheet, aligned to Common Core 7.EE.A.1.

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The kind of problems you'll get

Factor out the given factor from each expression. Show both quotients, then expand to check.

  1. Factor out 1/2 from 3/2 × m + 1

    Answer: 1/2 × (3 × m + 2)

  2. Factor out 2/3 from 8/3 × a − 2/3

    Answer: 2/3 × (4 × a − 1)

  3. Factor out −1/2 from 3/2 × x − 5/2

    Answer: −1/2 × (−3 × x + 5)

Every print pulls a fresh set of problems at this level, so a make-up test or a second sibling never gets the same sheet.

What's on a 7th grade sheet

Every version prints on US Letter or A4, with its answer key after the problems.

How to teach this

Ask your child to show each quotient before simplifying the expression inside the parentheses. Expanding the result checks both signs and values.

Watch for: Use the factor named in the question, even when another factor also works. Divide both terms by the factor, including its sign.

Common questions about 7th grade factoring out a specified rational factor

Is this the same as finding the greatest common factor?
The factor is supplied here. Students must use that exact factor; finding the greatest positive integer common factor is a separate lesson.
What does the key show?
By default, the key shows both quotients, the completed factorization and an expansion check at every difficulty. Choose Answers only for final answers without the worked steps.

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Aligned to Common Core 7.EE.A.1. Reviewed by the One more sheet team. Content version 241, updated October 2026.

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