| Factoring out common factors |
$(6x^2 + 3x) = 3x(2x + 1)$ |
When all terms share a common factor. |
| Sum–product pattern |
$(x^2 + 7x + 12) = (x + 3)(x + 4)$ |
When the expression is (x^2 + bx + c) and two factors of (c) add up to (b). |
| Grouping method |
$(2x^2 + 7x + 3) = (x + 3)(2x + 1)$ |
When the expression is $(ax^2 + bx + c)$ and two factors of (ac) add up to (b). |
| Perfect square trinomials |
$(x^2 + 10x + 25) = (x + 5)^2$ |
When the first and last terms are perfect squares and the middle term is twice their product. |
| Difference of squares |
$(x^2 - 9) = (x - 3)(x + 3)$ |
When the expression is a difference of two squares. |