Question

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

Answer 1

`5x^2 ( 3x + 2 ) ( x - 4 )`

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:

`5x^2 (3x^2 - 10x - 8)`

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 xx (-8)`).

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

`5x^2 ( 3x^2 - 12x + 2x - 8)`

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

`5x^2 (3x + 2)(x - 4)`