Reverse FOIL is factoring by thinking about how the trinomial was built: the First terms multiply to ax², the Last terms to c, and the Outer plus Inner terms give bx.
How to use the Reverse FOIL Calculator
- First coefficient (a)
- Second coefficient (b)
- Third coefficient (c)
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
The calculator finds integers whose product is a·c and whose sum is b, splits the middle term and groups. If no integer pair exists the trinomial is prime over the integers.
Formula
α·γ = a, β·δ = c, α·δ + β·γ = b
Worked example
Inputs — First coefficient (a): 6; Second coefficient (b): 11; Third coefficient (c): -35.
Results — Factored form = (3x − 5)(2x + 7); Roots = x = 1.666666667, x = −3.5; Steps = 1. Find two numbers whose product is a·c = −210 and whose sum is b = 11
2. They are −10 and 21. Split the middle term: 6x² − 10x + 21x − 35
3. Group and factor: 2x(3x − 5) + 7(3x − 5)
4. Result: (3x − 5)(2x + 7).
Key terms
- FOIL
- First, Outer, Inner, Last.
Frequently asked questions
What is reverse FOIL?
Factoring a trinomial into two binomials – undoing FOIL.
How do I start?
List factor pairs of a and of c and test which combination gives b.
What if no pair works?
The trinomial does not factor over the integers.
Is it the same as the ac method?
The ac method is a systematic way to do reverse FOIL.