# How do you factor 15x^4-50x^3-40x^2?

May 25, 2016

$5 {x}^{2} \left(3 x + 2\right) \left(x - 4\right)$

#### Explanation:

Look for the greatest common factors of all the numbers/letters. in this case, $5$ is common to $15$, $50$, and $40$, and ${x}^{2}$ for the $x$'s giving you:

$5 {x}^{2} \left(3 {x}^{2} - 10 x - 8\right)$

Since you have a number greater than $1$ for the ${x}^{2}$ inside the brackets, you can factor it further by determining what two number add up to $- 10$ and multiply to $- 24$ (derived from $3 \times \left(- 8\right)$).

$4$ and $6$ won't work because of the negative numbers, however, $- 12$ and $2$ will.

$5 {x}^{2} \left(3 {x}^{2} - 12 x + 2 x - 8\right)$

Look for the GCFs in the first two variables inside the brackets and then the second two.

5x^2 [ ( 3x (x - 4) + 2 (x - 4) ]

Collect like terms and simplify

$5 {x}^{2} \left(3 x + 2\right) \left(x - 4\right)$