Prove that the polynomial:

is continuous in

I was thinking of using the Delta Epsilon definition to show this but I couldn't figure out how to actually apply it (in the case of polynomials).

I was also thinking of proving it by induction since I saw a similar case where they showed that is continuous. So what I have so far is:

P(1) = a_1x^1 = a_1x which is continuous. ( I don't know if I should show that this actually is or if I can just assume it)

therefore assume that

is continuous.

thus

now since I assumed that P(x) is continuous, is the only thing that I have to show is that is continuous? If so would the Delta-Epsilon definition suffice?