Printable pre-algebra, algebra and geometry worksheets

Factoring Worksheets Generator

Make printable factoring practice for polynomials – from the greatest common factor to ax² + bx + c and grouping – with every answer fully factored in the key.

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A factoring worksheet gives you polynomials and asks you to rewrite each one as a product of simpler factors. This free factoring worksheet generator makes printable factoring worksheets with an answer key. It runs in your web browser, requires no sign-up, and uploads nothing, because the problems are made on your own device.

You can choose from seven problem types: greatest common factor, two kinds of trinomials (x² + bx + c and ax² + bx + c), difference of squares, perfect square trinomials, factoring by grouping, and mixed problems. Some books call the grouping type a factorisation (or factorization) by grouping worksheet; the mixed type is a general factorization of polynomials worksheet. For a prime factorization worksheet, see the GCF and LCM page. Everything you make here is free to use in class or in products you sell, such as Teachers Pay Teachers resources, Etsy printables or KDP workbooks.

Factoring worksheets example

How to use the Factoring Worksheet Generator

  1. Tick one or more boxes under Problem types. The Trinomials (x² + bx + c) box is ticked when the page opens.
  2. Choose a Difficulty: Easy, Medium or Hard.
  3. Choose the Number of problems: 6, 8, 10, 12, 15, 20, 24 or 30.
  4. Open More options to set the Columns (Automatic, 1, 2 or 3), the Paper size (Letter or A4), a Worksheet title, and whether to show a Name and date line. The Answer key on a separate page box is on by default.
  5. Check the preview on the right, which shows the sheet as it will print. Press Show answers to see each answer under its problem, and press again to hide them.
  6. Press New worksheet for a fresh random set with the same settings.
  7. Press Print / Save as PDF to open the print dialog. Choose “Save as PDF” there if you want a file.

When you tick several problem types, the problems are shared evenly between them and grouped by type, each group with its own one-line instruction. Problems are numbered 1 to N, and no problem repeats on one sheet. Copy link copies a link that reopens exactly the same worksheet. Your settings are remembered in this browser for your next visit, unless you open a shared link, which uses that link’s settings. The tool works on phones and tablets too. Printing needs a printer or the “Save as PDF” option.

How do you factor trinomials

To factor a trinomial, first take out the greatest common factor (GCF), then write the expression as a product of two binomials. For x² + bx + c, find two integers that multiply to c and add to b. For example, in x² + 8x + 12, the numbers 2 and 6 multiply to 12 and add to 8, so the answer is (x + 2)(x + 6). Negative numbers work the same way: in x² + x − 72, the numbers −8 and 9 give (x − 8)(x + 9).

When the leading coefficient a is greater than 1, use the ac method. Multiply a and c, then find two numbers that multiply to ac and add to b. Split the middle term with those numbers and factor by grouping. In 3x² + 7x + 2, ac = 6, and 6 and 1 add to 7. Rewrite 7x as 6x + x: 3x² + 6x + x + 2 = 3x(x + 2) + 1(x + 2) = (x + 2)(3x + 1). Trial and error also works. Hard problems often need a common factor taken out first. For example, 36x² − 12x − 224 = 4(3x − 8)(3x + 7).

What is factoring by grouping

Factoring by grouping is a method for polynomials with four terms. Group the terms into two pairs, factor the common part out of each pair, and then factor out the common binomial that remains. The binomial in both parts must match exactly. If it does not, rearrange the terms and try again.

For example, in x³ + 2x² + 6x + 12, the first pair has the common factor x² and the second pair has the common factor 6: x²(x + 2) + 6(x + 2). Both parts share (x + 2), so the answer is (x² + 6)(x + 2). A harder case is 6x³ − 3x² + 8x − 4. Factor the pairs to get 3x²(2x − 1) + 4(2x − 1), which gives (3x² + 4)(2x − 1).

Perfect square trinomials are a shortcut worth spotting: if the first and last terms are squares and the middle term is twice their product, as in 9x² + 12x + 4 = (3x + 2)², the answer is a binomial squared.

Sample problems from this generator

  1. x2 − 6x − 16 Answer: (x − 8)(x + 2)
  2. x2 − 14x + 48 Answer: (x − 8)(x − 6)
  3. x2 − 3x − 10 Answer: (x − 5)(x + 2)
  4. x2 − 3x − 4 Answer: (x − 4)(x + 1)

Frequently asked questions

How do you factor a difference of squares?

Use the pattern a² − b² = (a − b)(a + b). For example, x² − 64 = (x − 8)(x + 8). If there is a common factor, take it out first, as in 27x² − 147 = 3(3x − 7)(3x + 7).

How to check a factoring answer?

Multiply the factors back out using FOIL (First, Outer, Inner, Last). For (x + 2)(x + 6), you get x² + 6x + 2x + 12, which simplifies to x² + 8x + 12. That matches the original expression, so the answer is correct.

Is there an answer key?

Yes. The answer key is on by default and prints on a separate page after the worksheet, listing every problem number with its completely factored answer. To see answers on screen first, press Show answers in the preview.

Will every problem have a clean answer?

Yes. Every problem on these sheets factors over the integers, so each answer uses whole numbers in the factors.

Can I make more than one version of the same worksheet?

Yes. Press New worksheet to get different problems with the same settings. Teachers can print several versions for different groups. Use Copy link if you need to reopen one exact set later.

Does this work on a phone or tablet?

Yes. The generator works on phones and tablets as well as computers. You will need a printer or the Save as PDF option to print or save the sheet.

Can I use these factoring worksheets for commercial use?

Yes. Everything you make here is royalty-free for personal, classroom and commercial use, including Teachers Pay Teachers, Etsy printables, KDP workbooks and print-on-demand products. No credit is required. The only thing you may not do is copy the generator or the site itself to run a competing service. See the terms.