Question

If f(x)=x^5+5x^3+4, what is the remainder when f(x) is divided by x-2?

Answer 1

By the polynomial remainder theorem, the remainder is

f (2) = 2⁵ + 5×2³ + 4 = 32 + 40 + 4 = 76

(The theorem says a polynomial p(x) has remainder p(c) upon dividing it by x - c.)