Factoring Quadratics Made Simple
Factoring turns a quadratic into a product of two binomials. Learn the "sum and product" trick that makes it feel almost automatic.
Factoring is the reverse of expanding. Instead of multiplying two binomials together, we start with the quadratic and work backwards to find the binomials that produced it.
The sum and product method
For a quadratic in the form x² + bx + c, look for two numbers that multiply to c and add to b. For our example, we need two numbers that multiply to 6 and add to 5.
- 1List factor pairs of 6: 1 and 6, or 2 and 3.
- 2Which pair adds to 5? 2 + 3 = 5.
- 3Write the factors: (x + 2)(x + 3).
Why factoring matters
Once a quadratic is factored, solving equals zero becomes easy. If (x + 2)(x + 3) = 0, then either x + 2 = 0 or x + 3 = 0, giving x = -2 or x = -3. This is the zero product property, and it is one of the most useful tools in algebra.
Not every quadratic factors neatly with whole numbers — and that is exactly why the quadratic formula exists, which we cover in a separate lesson.
Written by Mathew Joane
Algebra teacher on a mission to make math feel less like memorizing and more like understanding.