Write a polynomial that satisfies the given conditions. Polynomial of lowest degree with zeros of 1/3 (multiplicity 2 ) and -5/6 (multiplicity 1 ) and with f(0) = -15

Question

This question always have me lost, I need help

Answer 1

(x-1/3)^2(x+5/6)

(a)(1/9)(5/6) = -15

a = (54/5)(-15) = -162

-162(x-1/3)(x-1/3)(x+5/6)

= -18(3x-1)^2(x+5/6)

=-3(3x-1)^2(6x+5)

=-3(9x^2 -6x +1)(6x+5)

--3(54x^3 +9x^2 -24x +5)

=-162x^3 -27x^2 + 72x -15