Question

How do you factor `5x^2-16x+12`?

Answer 1

`5x^2-16x+12 = (5x-6)((x-2)`

Explanation:

Hoping for rational factors, we note that
the only factors of `5` are `(1,5)`

So we are looking for values `a` and `b`
`color(white)("XXXX")` `(1x-a)(5x-b) = 5x^2 - (5a+b)x +ab`
such that `a*b = 12`
and `5a+b = 16`

The `(a,b)` factors of 12 are `(1,12), (2,6), (3,4), (4,3), (6,2), (12,1)`

We can check each pair for a pair that satisfies `5a+b = 16`
until we find `(a,b)=(2,6)`
which implies our factors are
`color(white)("XXXX")` `(x-2)(5x-6)`