Integrated Math 2 / Unit 2: Polynomials and Factoring
2.5 Factoring Trinomials: $ax^2 + bx + c$
Notes
When $a \neq 1$, use the ac method: find two numbers that multiply to $ac$ and add to $b$, split the middle term, then group.
- $2x^2 + 7x + 3$: $ac = 6$, numbers 1 and 6. $2x^2 + x + 6x + 3 = x(2x + 1) + 3(2x + 1) = (2x + 1)(x + 3)$.
- Always factor out a GCF first.
- Check by multiplying back.
Practice
Factor $2x^2 + 7x + 3$.
$ac = 6$ and the numbers 1 and 6 add to 7. Splitting and grouping gives $(2x + 1)(x + 3)$.
Factor $6x^2 - 5x - 4$.
Expand: $6x^2 + 3x - 8x - 4 = 6x^2 - 5x - 4$.
Factor $3x^2 + 10x - 8$.
$ac = -24$, numbers 12 and $-2$. Expand $(3x - 2)(x + 4) = 3x^2 + 12x - 2x - 8$.
Ready for more? Take the Unit 2 test.