Integrated Math 2 / Unit 2: Polynomials and Factoring
2.4 Factoring Trinomials: $x^2 + bx + c$
Notes
To factor $x^2 + bx + c$, find two numbers that multiply to $c$ and add to $b$.
- $x^2 + 7x + 12$: numbers 3 and 4, so $(x + 3)(x + 4)$.
- $x^2 - 2x - 24$: numbers $-6$ and $4$, so $(x - 6)(x + 4)$.
- If $c$ is positive, the two numbers have the same sign as $b$. If $c$ is negative, the signs differ.
- Check with FOIL.
Practice
Factor $x^2 + 7x + 12$.
$3 \cdot 4 = 12$ and $3 + 4 = 7$.
Factor $x^2 - 2x - 24$.
$-6 \cdot 4 = -24$ and $-6 + 4 = -2$.
A rectangle has area $x^2 + 9x + 20$. Which could be its length and width?
$4 \cdot 5 = 20$ and $4 + 5 = 9$.
Ready for more? Take the Unit 2 test.