We are given the polynomial
and asked to check if the binomial (p+8) is a factor of it. To check if it is, we will use the following:
Given a polynomial, the binomial (x - c) is a factor if and only if the polynomial takes the value of 0 when x=c.
So, in our case, we have that c=-8. So, the binomial (p+8) is a factor of the given polynomial, if and only if, it takes the value of 0 when p=-8.
We can check that
so this means that the binomial (p+8) is a factor of the given polynomial