# How do you factor  -x^2+7x+18?

May 12, 2015

$f \left(x\right) = - {x}^{2} + 7 x + 18 = - \left(x - p\right) \left(x - q\right)$

Use the new AC Method to factor trinomials.
Compose factor pairs of (c = 18) and look for the pair whose sum is
(b = 7). Proceed: (-1, 18)(-2, 9). Since a < 0, Then, p = 2 and q = -9.
Factored form:

$f \left(x\right) = - \left(x + 2\right) \left(x - 9\right)$

Check: Develop f(x) = -(x^2 - 7x - 18) = -x^2 + 7x + 18. Correct.