algebra
Factoring Quadratic Equations
The Factoring Method
1
Find two numbers that...
Multiply to give "c" AND Add to give "b"2
For x² - 5x + 6 = 0
Need: multiply to 6, add to -5 → (-2) and (-3)3
Write in factored form
(x - 2)(x - 3) = 04
Set each factor = 0
x - 2 = 0 → x = 2, x - 3 = 0 → x = 3💡When Does Factoring Work?
Factoring works best when the roots are nice integers or simple fractions. If you can't find factors quickly, use the quadratic formula instead — it always works!
More Examples
x² + 7x + 12 = 0
(x + 3)(x + 4) = 0
x = -3, -4
x² - x - 6 = 0
(x - 3)(x + 2) = 0
x = 3, -2
x² - 9 = 0
(x - 3)(x + 3) = 0
x = 3, -3
Special Patterns
Difference of Squares:
x² - a² = (x - a)(x + a)Perfect Square:
x² + 2ax + a² = (x + a)²⚠️ Common Mistakes
- Sign errors — watch the positive/negative!
- Not checking your factors by expanding back
- Forgetting to set each factor equal to zero