Question

Is x-3 a factor of `x^3-6x^2-x+30`?

Answer 1

If `a` is a root of a polynomial `P(x)` (that is `P(a)=0`), then `P(x)` is divisible by `(x-a)`

Explanation:

So, we need to evaluate `P(3)`. That is:

`3^3-(6*3^2)-3+30=27-54-3+30=27-57+30=0`

and so the polynomial give is divisible by `(x-3)`