Factoring ax² + bx + c — Cheat sheet

Key method

For $ax^2+bx+c$, seek numbers whose product is $ac$ and sum is $b$. If none exist among integers, use the discriminant or quadratic formula rather than forcing integer factors.

Example

Factor $6x^2+11x+3$. The product $ac=18$ and sum $b=11$ suggest $9$ and $2$:

Hence $(3x+1)(2x+3)$. The two zeros are $-1/3$ and $-3/2$.

Avoid this mistake

Matching only the constant term is insufficient. Check the middle coefficient as well as the leading coefficient.