# How do you factor -2x^3 + 4x^2 +96x?

Aug 28, 2015

#### Answer:

-2x^3 + 4x^2 +96x = color(green)(-2x(x + 6)(x - 8)

#### Explanation:

Factorizing an expression is to write it as a product of its factors

The first step of factorizing an expression is to 'take out' any common factors which the terms have.

In the given expression, we can take out $- 2 x$ as a common factor

-2x^3 + 4x^2 +96x = -2xcolor(blue)((x^2 - 2x - 48)

And now we factorize color(blue)((x^2 - 2x - 48)

We can use Splitting the middle term technique to factorise the above expression

color(blue)(x^2 - 2x - 48x
$= {x}^{2} + 6 x - 8 x - 48$

$= x \left(x + 6\right) - 8 \left(x + 6\right)$

As $x + 6$ is common to both the terms, we can write the expression as: color(blue)((x + 6)(x - 8)

Hence we get -2x^3 + 4x^2 +96x = color(green)(-2x(x + 6)(x - 8)