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

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Answer 1 · 2015-08-28T08:49:14

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

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

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