Reverse FOIL Calculator

Reverse FOIL Calculator

Factor a quadratic trinomial by splitting the middle term and grouping the terms that share a common factor.

Last updated: June 2026 | By Patchworkr Team

The grouping step did not produce matching binomial factors.
Factored form
Enter a trinomial to factor

What Is Reverse FOIL?

Reverse FOIL is a factoring method for quadratic trinomials. It works by finding two numbers that multiply to ac and add to b, then splitting the middle term and factoring by grouping.

How To Factor A Trinomial

  1. Multiply a and c.
  2. Find two integers that multiply to ac and add to b.
  3. Split the middle term using those two integers.
  4. Factor by grouping.
ax^2 + bx + c

Worked Example

x^2 - 5x + 6 factors to (x - 2)(x - 3).

ac = 6
2 + 3 = 5
(x - 2)(x - 3)

Frequently Asked Questions

What if the trinomial is not factorable?

The calculator returns a message instead of forcing a false factorization.

Does this work with non-integer coefficients?

No. This version is designed for integer coefficients only.

Why are there two possible splits?

Because the middle term can often be split in more than one order before factoring.

Does the leading coefficient have to be 1?

No. The calculator supports general quadratic trinomials.

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