3rd degree polynomials

Question

Give a third degree polynomial that has zeros of 13, 5i, and -5i, and has a value of -680 when x = 3. Write the polynomial in standard form.

Answer 1

(x-13)(x^2+5) =

x^3 -8x^2 - 65 works except for the constant term

f(3) = 3^3 -8(3^2) -65 = -110 when you need -680

so multiply by 680/110 = 68/11

f(x) = 68x^3/11 - 544x^2/11 - 65(68)/11

f(x) = (68/11)x^3 - (544/11)x^2 - 4420/11