PEAZIT Aha card
Go straight to resources ↓Factoring: put the common factor outside
Factoring reverses expansion. Divide each original term by the common factor; put the quotients inside the brackets.
| Expression | Meaning |
|---|---|
| 6x² + 9x | The common factor is 3x. |
| 6x²/(3x) = 2x; 9x/(3x) = 3 | Find the remaining factors. |
| 3x(2x + 3) | Expanding checks the original sum. |
One worked example
- 6x² + 9xThe common factor is 3x.
- 6x²/(3x) = 2x; 9x/(3x) = 3Find the remaining factors.
- 3x(2x + 3)Expanding checks the original sum.
Watch out: The factorisation identity also holds at x = 0; division here finds factors. When solving an equation, do not divide by x without checking zero.
Goal, prerequisites and card origin
What you will learn: Factor a sum by taking out its common factor.
What you need first: Multiplying expressions and expanding brackets.
An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1
Show connections
Factoring reverses expansion. Divide each original term by the common factor; put the quotients inside the brackets.