How to Use Reverse FOIL Calculator
The Reverse FOIL Calculator factors a quadratic trinomial into two binomials in three simple steps. Enter integer coefficients and read the factored result immediately.
- Enter coefficient a - The leading coefficient of x² (must not be zero).
- Enter coefficient b - The coefficient of the middle term x.
- Enter coefficient c - The constant term.
- Review the result - The Reverse FOIL Calculator shows the factored form, a step-by-step AC-method walkthrough, and an expansion verification.
For example, entering a = 1, b = 5, c = 6 gives (x + 2)(x + 3). Entering a = 2, b = 7, c = 3 gives (2x + 1)(x + 3).
Formula & Theory - Reverse FOIL Calculator
The Reverse FOIL Calculator applies the AC factoring method:
ax² + bx + c
Step 1: Compute a × c
Step 2: Find two integers m, n such that m × n = ac and m + n = b
Step 3: Rewrite bx as mx + nx
Step 4: Factor by grouping| Symbol | Meaning |
|---|---|
| a | Leading coefficient |
| b | Middle coefficient |
| c | Constant term |
| m, n | Factor pair satisfying m × n = ac, m + n = b |
Discriminant check:
Before searching for integer factors, the Reverse FOIL Calculator evaluates the discriminant Δ = b² − 4ac. If Δ is not a non-negative perfect square integer, integer factoring is impossible.
Assumptions and Limits
Inputs must be integers. Non-integer coefficients such as fractions or decimals are not supported for factoring over the integers. If you need to factor over the rationals, use the quadratic formula instead.
Use Cases for Reverse FOIL Calculator
The Reverse FOIL Calculator is a practical tool for algebra students and teachers. Common uses include:
- Algebra class - Factor x² + 7x + 12 = (x + 3)(x + 4) to solve a quadratic equation by setting each factor to zero.
- FOIL practice - Use the factored form to practice the forward FOIL expansion as a self-check.
- Homework verification - Confirm that your manual factoring attempt is correct with the expansion verification step.
- Test preparation - Quickly test many trinomials to develop pattern recognition for factoring.
The expansion verification shown by the Reverse FOIL Calculator confirms the result by multiplying the two binomials back together, ensuring no arithmetic errors were made.