A. Here's a fifth degree polynomial,
f(x) = x⁵ + 4x⁴ - 14x² + 9
It's in standard form, each term a constant coefficient times a whole number power of x (including the constant, which we can think of as the coefficient on x⁰=1), with the terms sorted from highest degree (highest power on x) to lowest.
B. The closure of addition wrt polynomials just means when we add two polynomials we get another polynomial.
f(x) = x⁵ + 4x⁴ - 14x² + 9
g(x) = -2x⁴ + x
f(x)+g(x) = x⁵ + 2x⁴ - 14x² + x + 9
We added two polynomials, we got another one, that's all closure is.
