Question

How do you factor # (15x²+22x-5)?

Answer 1

In an attempt to find integer based factors:
We are looking for factors of 15 `(axxb)`
and factors of 5 `(cxxd)`
such that `ac-bd = 22`

There are only a very few factors available and we should soon come up with `(a,b)=(5,3)` and `(c,d)=(5,1)`

Since the final term of the given expression is negative, one of `(5,1)` needs to be negative;
furthermore, since the coefficient of the middle term is positive
5 must be the positive value and 1 the negative.

Factors:
`15x^2+22x-5=(5x-1)(3x+5)`