Taking out a common factor, step by step
The first thing to try on any expression: does every term share a factor?
24x² + 120x + 168
- Before anything else, look at whether every term shares a factor. The numbers here are 24, 120, 168 — so the question is what the biggest number that divides ALL of them is.
- List what divides each one and look for the biggest they all share. 24: 1, 2, 3, 4, 6, 8, 12, 24 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 168: 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168.
- The biggest number in all of those lists is 24. Take it out in front and divide every term by it: 24 ÷ 24 = 1, 120 ÷ 24 = 5, 168 ÷ 24 = 7.
- Check the bracket before you stop. x² + 5x + 7 — those numbers share nothing but 1, so there is no more to take out and 24 really was the greatest. 24x² + 120x + 168 = 24(x² + 5x + 7).
How it works.
- 01
Before anything else, look at whether every term shares a factor. The numbers here are 24, 120, 168 — so the question is what the biggest number that divides ALL of them is.
- 02
List what divides each one and look for the biggest they all share. 24: 1, 2, 3, 4, 6, 8, 12, 24 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 168: 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168.
- 03
The biggest number in all of those lists is 24. Take it out in front and divide every term by it: 24 ÷ 24 = 1, 120 ÷ 24 = 5, 168 ÷ 24 = 7.
- 04
Check the bracket before you stop. x² + 5x + 7 — those numbers share nothing but 1, so there is no more to take out and 24 really was the greatest. 24x² + 120x + 168 = 24(x² + 5x + 7).