Question

How do you factor the expression `15x^2-2x-8`?

Answer 1

`(5x-4)(3x+2)`
`15x^2-12x+10x-8`

Explanation:

Check for a product what product:
`(-2-3x) (4-5x)`
Multiply and test:
`-8-12x+10x+15x^2`
Multiply by negative one if you like and have the factors in the answer form
Wich recovers the original quadratic equation

Answer 2

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

Explanation:

First, you have to find the zeros of the expression, with the general expression

`x=(-b+-sqrt(b^2-4ac))/(2a)`

`x=(2+-sqrt(2^2-4*15*8))/(2*15)`

`x=(2+-sqrt(484))/(30)`

`x=(2+-22)/(30)`

`x=24/30` or `x=-20/30`

`x=4/5` or `x=-2/3`

Finding the zeros we can factorize the expression:

`15(x-4/5)(x+2/3)`

We can continue further to

`5(x-4/5)*3(x+2/3)`

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