## Using the Quadratic Formula to Solve FOIL Factoring

### Algebra: FOIL Help

#### Home | FOIL menu | Algebra menu

**Example:** Factor
-2x^{2}+19x-24.

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

-2x^{2}+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 ^{2}.

So -2x^{2}+19x-24 = (x-8)(-2x +3).

## Algebra: FOIL Help

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