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Example: Factor -2x²+19x-24.

Step 1: Set this expression equal to 0. We get

-2x²+19x-24 = 0

What we want is to do is use the quadratic formula to solve for the roots of the equation.
We have a = -2, b = 19, and c = -24. Plugging these numbers into the quadratic formula we get:

One root is (-19-13)/-4 = 8. The other root is (-19+13)/-4 = 3/2. We then have:

or

(x-8)(-2x +3) = 0

because we want the first term of our expanded FOIL expression to multiply to -2x².
So -2x²+19x-24 = (x-8)(-2x +3).