• Free
  • Grade 9
  • Two terms or three

Taking out a common factor worksheets

The first thing to try on any expression: does every term share a factor? These free printable worksheets take it out.

Kid stuck on one? You don’t just get the sheet.

  • Answer key included
  • Reopen this exact sheet
  • Letter & A4 ready
Ready to printTaking out a common factor
Taking out a common factor worksheet — Two terms or three, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

This is the step students skip on the way to everything else. Before factoring a quadratic or solving anything, look at whether every term shares a factor and pull it out in front — and if you do not, every later step is bigger than it needed to be.

Why this sheet works

The word that carries the difficulty is GREATEST. 6x + 12 has 2 in common, and 3, and 6; only the last one finishes the job, and a student who stops at 2 writes 2(3x + 6), which still has a 3 inside. So the walks list what divides each coefficient and take the biggest they share, rather than announcing a number — listing is short, checkable, and repeatable on the next question.

How this one works

One question from this sheet, worked through a step at a time.

68x² + 136x + 85

68x² + 136x + 85
6813685
68:124173468
136:1248173468136
85:151785
17 × (4x² + 8x + 5)
68x² + 136x + 85=17(4x² + 8x + 5)
  1. Before anything else, look at whether every term shares a factor. The numbers here are 68, 136, 85 — so the question is what the biggest number that divides ALL of them is.
  2. List what divides each one and look for the biggest they all share. 68: 1, 2, 4, 17, 34, 68 136: 1, 2, 4, 8, 17, 34, 68, 136 85: 1, 5, 17, 85.
  3. The biggest number in all of those lists is 17. Take it out in front and divide every term by it: 68 ÷ 17 = 4, 136 ÷ 17 = 8, 85 ÷ 17 = 5.
  4. Check the bracket before you stop. 4x² + 8x + 5 — those numbers share nothing but 1, so there is no more to take out and 17 really was the greatest. 68x² + 136x + 85 = 17(4x² + 8x + 5).