Question

Can `y= 3x^2-30x-72` be factored? If so what are the factors ?

Answer 1

Yes.
Factors are: `3, (x-12), (x+2)`

Explanation:

`y = 3x^2-30x-72`
By inspection, 3 is a factor `-> y=3(x^2-10x-24)`

Since the constant term is `-24` and the coefficient of `x` is `-10`, we now look for factors of `24` which differ by `10`

These are 12 and 2.

Since the constant term is `-ve` the constants in the factors must have different sign. Also, since the coefficient of `x` is also `-ve` the larger factor of `24` must be `-ve`.

Hence the second and third factors are `(x-12) and (x+2)`

Therefore: `y =3(x-12)(x+2)`