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

Real roots: −1, 1, 3 and (2,f(2))=(2,5)

\(\text{the polynomial will be of the form}\\ p(x) = k(x+1)(x-1)(x-3) \\ p(2) = k(3)(1)(-1) = 5 \\ -3k = 5 \\ k=-\dfrac 5 3 \\ p(x) = \dfrac 5 3 (x+1)(x-1)(x-3) \\ p(x) = -\dfrac{5 x^3}{3}+5 x^2+\dfrac{5 x}{3}-5\)