Construct a polynomial function of least degree

Question

Construct a polynomial function of least degree possible using the given information.

Real roots: −1, 1, 3 and (2, f(2)) = (2, 7)

Answer 1

f(x) = a(x + 1)(x - 1)(x - 3); f(2) = a(2 + 1)(2 - 1)(2 - 3) = 7; - 3a = 7; a = - 7/3;

f(x) = -7/3(x + 1)(x - 1)(x - 3)