college algebra

Question

Find a polynomial function of degree 3 with real coefficients that satisfies the given conditions. Zero of −3 having multiplicity​ 3; f(3​)=36.

f(x)= ?

Answer 1

(x+3)^3

= x^3 + 3x^2 + 9x + 27

f(3) = (3+3)^3 = 6^3 = 36(6) = 216 Not 36

but add (1/6) as a factor

(1/6)(x+3)^3

then f(3) = (1/6)(3+3)^3 = (1/6)(6^3) = 6^2 = 36

polynomial of degree 3 with zero of -3 and f(3) = 36

is (1/6)x^3 + (1/2)x^2 + (3/2)x + 9/2