If f(k)=0 for some polynomial, then by the factor theorem (x-k) is a factor, not (x+k).
So the answer is false.
For example, for the polynomial `f(x)=x^2-2x+1 ` we have f(1)=0, but (x+1) is not a factor since `x^2-2x+1=(x-1)^2 ` ; the only factor is (x-1).
It is true. (My mom told me).