Write a polynomial f(x) that satisfies the given conditions. Polynomial of lowest degree with zero of -4 (multiplicity 1), 1 (multiplicity 1), and with f(0)=16

Answer 1

If c is a root, then x - c is a factor

f(x) = a(x+4)(x-1)

Since f(0) = 16, we have -4a = 16. so, a = -4.

Therefore, f(x) = -4(x+4)(x-1) = -4(x² + 3x - 4) = -4x² - 12x +16