Question

How do you factor `15x^2 – 25x – 60`?

Answer 1

`15x^2-25x-60=5(3x+4)(x-3)`

Explanation:

To factorize a polynomial of general form `ax^2+bx+c`, one should divide middle term `bx` in two parts, whose sum is `b` and product is `axxc`.

So for `15x^2-25x-60`, we should divide `-25x` in two parts which add up to `-25` and whose product is `15xx(-60)=-900`.

A few trial indicate them to be `-45` and `20`. Hence

`15x^2-25x-60=15x^2-45x+20x-60` or

`15x(x-3)+20(x-3)` or

`(15x+20)(x-3)` or `5(3x+4)(x-3)`