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

1 Answer
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 #-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)#