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

Question

2095 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-04-01T20:48:55

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

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:

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

How do you factor 25x^2-10x-1525x^2-10x-15?