Factor Trinomials With Leading Coefficient Greater Than One

Goal Factor a trinomial whose leading coefficient is greater than 1.

1) Identify the trinomial form Look for an expression like ax^2 + bx + c, where a > 1. The goal is to rewrite it as a product of two binomials.

2) Use the product-sum idea Find two numbers that:

• multiply to a × c
• add to b

These numbers help you split the middle term.

3) Split and group Rewrite the trinomial using the two numbers found, then group the terms in pairs. Factor out the greatest common factor from each group.

4) Finish factoring If the two groups now share the same binomial factor, factor that binomial out. Your answer should be fully simplified.

5) Check your result Multiply the binomials back together. If you recover the original trinomial, the factorization is correct.

Helpful tips

• Look for common factors first; factor them out before trying to split the middle term.
• Watch signs carefully. A negative middle term means one of the two numbers is negative.
• If the trinomial does not factor nicely with integers, recheck the number pair and the common factor work.

Example pattern ax^2 + bx + c → (mx + n)(px + q) where the two binomials expand back to the original expression.