Math July 13, 2026 · 8 Min Read

Reverse FOIL Calculator – Guide & Formulas

Factor quadratic trinomials using reverse FOIL. Enter ax² + bx + c to see factored form (px + q)(rx + s) with step-by-step solutions.

Factor any quadratic trinomial using reverse FOIL with our free online calculator. Enter ax² + bx + c to see the factored form and step-by-step breakdown.

Key Takeaway

Use the free Reverse FOIL Calculator to factor quadratic trinomials using reverse foil. enter ax² + bx + c to see factored form (px + q)(rx + s) with step-by-step solutions. Get instant results with step-by-step explanations.

How to Use the Reverse FOIL Calculator

  1. Step 1: Enter the coefficient a (of x²)
  2. Step 2: Enter the coefficient b (of x)
  3. Step 3: Enter the constant c
  4. Step 4: Click Factor to see the factored form and solution steps

The Formula

Reverse FOIL: Find two binomials (px + q) and (rx + s) whose product equals the original trinomial. The coefficients satisfy: p×r = a, q×s = c, and p×s + q×r = b.

Variable Definitions

  • a: Coefficient of the x² term
  • b: Coefficient of the x term
  • c: The constant term
  • p, r: Factors of a (leading coefficient)
  • q, s: Factors of c (constant term)
  • FOIL: First, Outer, Inner, Last — the method for multiplying binomials

Factoring x² + 5x + 6

Factor the trinomial x² + 5x + 6 using reverse FOIL.

  1. Step 1: Identify a = 1, b = 5, c = 6
  2. Step 2: Find factors of c = 6 that add to b = 5: (2, 3) since 2 + 3 = 5
  3. Step 3: Since a = 1, the factored form is (x + 2)(x + 3)
  4. Step 4: Verify by expanding: (x + 2)(x + 3) = x² + 3x + 2x + 6 = x² + 5x + 6 ✓

Frequently Asked Questions

What is the FOIL method?

FOIL stands for First, Outer, Inner, Last — the four products you multiply when expanding (a+b)(c+d) = ac + ad + bc + bd. Reverse FOIL undoes this process.

What if a ≠ 1?

When a ≠ 1, you need to find factors of a×c that add to b, then use factoring by grouping. For example, 2x² + 7x + 3 = (2x + 1)(x + 3).

Can all trinomials be factored?

No. Some trinomials are prime (irreducible) over the integers, meaning they cannot be factored into integer binomials. The discriminant b² - 4ac < 0 or not being a perfect square indicates this.

How do I know if a trinomial can be factored?

Check the discriminant: D = b² - 4ac. If D is a perfect square, the trinomial factors over integers. If D < 0, it has no real roots and cannot be factored over reals.

What is factoring by grouping?

When a ≠ 1, split the middle term bx into two terms whose coefficients multiply to a×c and add to b, then group and factor common terms from each pair.