8.5 Factoring Trinomials: $x^2 + bx + c$

Notes

To factor $x^2 + bx + c$, find two numbers that multiply to $c$ and add to $b$.

• $x^2 + 7x + 12$: $3 \cdot 4 = 12$ and $3 + 4 = 7$, so $(x + 3)(x + 4)$.
• If $c$ is negative, the numbers have opposite signs: $x^2 - 2x - 15 = (x - 5)(x + 3)$.
• If $c$ is positive and $b$ is negative, both numbers are negative: $x^2 - 9x + 20 = (x - 4)(x - 5)$.