Question

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

Answer 1

`-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 `-2x` 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 + 6x - 8x - 48`

`= x(x+6) - 8(x+6)`

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)`