What applies here is one of the laws of the factorization of polynomials, called the factor theorem and it states that:
For a polynomial f(x) , if for any value a, f(a) =0 then (x-a) is factor of f(x)
Example:
Consider the polynomial
[tex]f(x) = x^{3} - 3x^{2} - 8x+4[/tex]
For a =3,
[tex]f(a) = (3)^{3} - 3(3)^{2} - 8(3)+24[/tex]
= 27-27-24+24 = 0
f (3)= 0
which means (x-3) is a factor of f(x)
Applying the above rule to the question:
if (x + 3) is a factor of a polynomial f(x), then f(-3) = 0
note that (x+3) can also be written as (x- (-3)).
