In order to find if each binomial is a factor of the given polynomial function, we can use the zero remainder theorem.
This theorem states that if a value x = k is a zero of the function f(x) (that is, f(k) = 0), so the binomial (x - k) is a factor of the function f(x).
Therefore, let's check the values 1, 3, -3, 4 and -4:
[tex]\begin{gathered} f(1)=1+4-9-36=-40 \\ f(3)=27+36-27-36=0 \\ f(-3)=-27+36+27-36=0 \\ f(4)=64+64-36-36=64 \\ f(-4)=-64+64+36-36=0 \end{gathered}[/tex]
Therefore the answer is:
(x - 1): No
(x - 3): Yes
(x + 3): Yes
(x - 4): No
(x + 4): Yes
