Find the polynomial function of degree 3 with real coefficients that satisfies given conditions; zero of −4 and zero of 0 having multiplicity 2 where 𝑓(−1) = 6

Question

Find the polynomial function of degree 3 with real coefficients that satisfies given conditions; zero of −4 and zero of 0 having multiplicity 2 where 𝑓(−1) = 6

Answer 1

f(x) = A(x + 4)(x - 0)²

f(x) = Ax²(x + 4)

6 = A(-1)²(-1 + 4)

6 = 3A

A = 2

f(x) = 2x²(x + 4)