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

Question

1994 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-08-28T08:49:14

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

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 $- 2 x$ $-2x$ as a common factor

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

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

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

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

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

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

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

How do you factor -2x^3 + 4x^2 +96x−2x3+4x2+96x-2x^3 + 4x^2 +96x?