math 126 pre-calculus

Question

Find a formula for the polynomial P(x) with

1. degree 3
2. real coefficients
3. zeros at x=2+4i and x=-6
4. y-intercept at (0,-360) 

Answer 1

x=2+4i

x-2=4i

x^2-4x+4= -16

x^2-4x-12=0

y=-360=P(0)=a(x^2-4x-12)(x+6)= a(-12)(6)=-72a

a=360/72= 5

P(x)=5(x+6)(x^2-4x-12)

and if you want multiply it out to get

5(x^3+2x^2-36x-72)

P(x) = 5x^3+10x^2 -180x -360