Question

How do you factor `5x^2 - 7x + 2`?

Answer 1

First notice that `1` is a root of `5x^2-7x+2 = 0` so `(x-1)` is a factor.

So we can split the middle term as follows:

`5x^2-7x+2`

`= 5x^2-5x-2x+2`

`= 5x(x-1)-2(x-1)`

`= (5x-2)(x-1)`