Construct a polynomial function of least degree possible using the given information. Real roots: −1, 1, 3 and (2, f(2)) = (2, 8)

Answer 1

(x+1)(x-1)(x-3) = (x^2-1)(x-3) = x^3 -3x^2 -x +3

(2,8) is on the curve

f(2) = 8 = a[(2)^3 -3(2)^2 -2 + 3]= a[8-12-2] = -6a

a = 8/-6 = -4/3

f(x) = (-4/3)x^3 +4x^2 +4x/3 -4