Question

How do you factor `25x^2-10x-15`?

Answer 1

`25x^2-10x-15 = 5(x-1)(5x+3)`

Explanation:

First note that all of the terms are divisible by `5` so separate that out as a factor first:

`25x^2-10x-15 = 5(5x^2-2x-3)`

Next notice that the sum of the coefficients of the remaining factor is zero. That is: `5-2-3 = 0`. So `x=1` is a zero and `(x-1)` a factor:

`5x^2-2x-3 = (x-1)(5x+3)`

Putting it all together:

`25x^2-10x-15 = 5(x-1)(5x+3)`