$p(x)$ Polynom with degree $k$, show each integrable function $a(x)$, the convolution $a(x) * p(x)$ is a polynom of max degree $k$

Question

As title says, I will try to make it more clearer here:

Let $p(x)$ be a Polynom with degree k, for example: $x^k$ ( I think ).
Show each Integrable function $a(x)$, the convolution $a(x)*p(x)$ is a polynom with most degree of $k$.

What I understand from here, I need to prove that the convolution of two Polynom with a max degree of K is max degree of K or lower.

Problem is, how do I start? I dont know how I should get on with this question . I cant just do convolution between two polynoms, since I dont have their functions themselves, but a parameter.
Any thing that will help me answer will be good ( How to start ).