Let $g(x) = x^5 + x^4 + x^3 + x^2 + x + 1$. what is the remainder when the polynomial $g(x^{12})$ is divided by the polynomial $g(x)$?

Find the roots of the polynomial function f(x) = x^3 + 2x^2 + x

Consider the set of all four-digit positive integers less than 2000 whose digits have a sum of 24. what is the median of this set of integers?

Over which interval is the graph of f(x) = x2 + 5x + 6 increasing?