Reverse FOIL (Factoring) Calculator
Factor a quadratic expression ax² + bx + c into (mx + n)(px + q). Reverse FOIL method.
Formula
ax² + bx + c = (mx + n)(px + q); solve using discriminant
- Discriminant Δ = b² - 4ac
- Factorable if Δ ≥ 0 and √Δ is integer
- Roots: x = (-b ± √Δ) / 2a
- If not factorable, use quadratic formula for decimal roots
Example
Inputs
- Coefficient a (x²): 1
- Coefficient b (x): 5
- Constant c: 6
x² + 5x + 6 = (x + 2)(x + 3); discriminant = 1 (perfect square)
Frequently asked questions
When is a quadratic factorable?
When the discriminant is a perfect square (non-negative integer).
What if it's not factorable?
Use the quadratic formula to find decimal roots: x = (-b ± √Δ) / 2a