polynomial function of least degree

Question

construct a polynomial function of least degree possible using the given information

Real roots: -2,1/2 (with multiplicity 2) and (-3,f(-3)) = (-3,5)

Answer 1

f(x) = (x+2)(x-1/2)^2/3.5

f(-3) = -(3.5)^2/3.5 = -3.5

f(x) = (x+2)(x^2 +x + 1/4)/3.5

= (x^3 +3x^2 +9x/4 + 1/2)/3.5

= x^3/3.5 +3x^2/3.5 +9x/14 + 7/4

= 2x^3/7 + 6x^2/7 + 9x/14 + 7/4