Math
Factoring trinomials.
Definition
Factoring trinomials means rewriting a quadratic expression ax² + bx + c as a product of two binomials. When a = 1, find two numbers that multiply to c and add to b. When a ≠ 1, use the AC method or trial and error.
How it works · 4 phases
Step by step.
- If a = 1: find two numbers that multiply to c and add to b
- Write as (x + m)(x + n) where m and n are those numbers
- If a ≠ 1: find two numbers that multiply to ac and add to b
- Rewrite the middle term using those two numbers and factor by grouping
Examples
Real-world.
- 1 x² + 7x + 12 = (x + 3)(x + 4)
- 2 x² - 5x + 6 = (x - 2)(x - 3)
- 3 2x² + 7x + 3 = (2x + 1)(x + 3)
Key Fact
For x² + bx + c, find m and n where mn = c and m + n = b.