How do you use factor theorem to show an algebraic term is a factor of a polynomial?

For example show that x + 3 is a factor of p(x) = x³ - 5x² - 8x + 48

We need to show that when x = -3, p(x) = 0. If this is the case then x + 3 is a factor of p(x)

putting x = -3 into the polynomial we obtain:

p(x) = - 27 - 45 + 24 + 48 = 0 therefore x + 3 is a factor of p(x).