We are given the polynomial
[tex]p^3+14p^2+49p+8[/tex]
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
[tex](-8)^3+14\cdot(-8)^2+49\cdot(\text{ -8)+8= -512+14}\cdot64-392+8=\text{ -512+}896\text{ -392 +8=}0[/tex]
so this means that the binomial (p+8) is a factor of the given polynomial
