Algebra 1 / Unit 8: Polynomials and Factoring
8.6 Factoring Trinomials: $ax^2 + bx + c$
Notes
When $a \ne 1$, use the AC method: 1. Multiply $a \cdot c$. 2. Find two numbers that multiply to $ac$ and add to $b$. 3. Split the middle term with them and factor by grouping. Example: $2x^2 + 7x + 3$. $ac = 6$; $1 \cdot 6 = 6$ and $1 + 6 = 7$. $2x^2 + x + 6x + 3 = x(2x + 1) + 3(2x + 1) = (x + 3)(2x + 1)$.
Practice
Factor $3x^2 + 10x + 8$.
Check: $3x^2 + 6x + 4x + 8$.
Factor $2x^2 - 5x - 3$.
$ac = -6$: $-6$ and 1 add to $-5$.
Factor completely: $4x^2 + 14x + 6$.
GCF 2 first: $2(2x^2 + 7x + 3)$.
Ready for more? Take the Unit 8 test.