Reverse FOIL Calculator
Factor quadratic expressions using the reverse FOIL method with step-by-step solutions
Factor Quadratic Expression
Enter coefficients for the quadratic expression:
Coefficient of x² (cannot be zero)
Coefficient of x (middle term)
Constant term
Factorization Result
Step-by-Step Solution
The expression 1x² is already in simplest form
Example: Factor 6x² - 7x - 5
Given Expression
6x² - 7x - 5
a = 6, b = -7, c = -5
Solution Steps
1. Find factors of a = 6: -6
2. Find factors of c = -5: 5
3. Try α = 2, γ = 3, β = 1, δ = -5
4. Check: outer = 2 × (-5) = -10, inner = 1 × 3 = 3
5. Sum: -10 + 3 = -7 ✓ (matches b coefficient)
Result: 6x² - 7x - 5 = (2x + 1)(3x - 5)
FOIL Method
First
Multiply first terms
ax × cx = acx²
Outer
Multiply outer terms
ax × d = adx
Inner
Multiply inner terms
b × cx = bcx
Last
Multiply last terms
b × d = bd
Factoring Tips
Look for common factors first
Find all factor pairs systematically
Check your work by expanding
Consider negative factors
Some expressions are prime (unfactorable)
Understanding the Reverse FOIL Method
What is Reverse FOIL?
The reverse FOIL method is a factorization technique used to factor quadratic trinomials of the form ax² + bx + c into the product of two binomials. It's called "reverse" because it undoes the FOIL multiplication process.
When to Use It?
- •Solving quadratic equations
- •Simplifying rational expressions
- •Finding roots of parabolas
- •Graphing quadratic functions
The Process
For ax² + bx + c = (αx + β)(γx + δ):
- 1. Find factors of 'a' for α and γ
- 2. Find factors of 'c' for β and δ
- 3. Check if αδ + βγ = b
- 4. Verify by expanding
Special Cases
- Perfect Square: a² + 2ab + b² = (a + b)²
- Difference of Squares: a² - b² = (a + b)(a - b)
- Prime Expression: Cannot be factored over integers