Quartic functions.

[keeyla]

Hello! Ok so I have done this problem but I am not sure if I am doing this right. If someone could just let me know whether I am heading in the right direction or not that would be superb!
The question is:

Sketch an example of a quartic function with the given zeros. Then write an equation of the function.
-2,1,3,6

This is what I did.

(x+2)(x-1)(x-3)(x-6)

(x+2)(x-1) (x-3)(x-6)
x[sup:2zetr3r8]2[/sup:2zetr3r8]-x+2x-2 x[sup:2zetr3r8]2[/sup:2zetr3r8]-6x-3x+18
(x[sup:2zetr3r8]2[/sup:2zetr3r8]+x-2)(x[sup:2zetr3r8]2[/sup:2zetr3r8]-9x+18)
x[sup:2zetr3r8]4[/sup:2zetr3r8]-9x[sup:2zetr3r8]3[/sup:2zetr3r8]+18x[sup:2zetr3r8]2[/sup:2zetr3r8]+x[sup:2zetr3r8]3[/sup:2zetr3r8]-9x[sup:2zetr3r8]2[/sup:2zetr3r8]+18x-2x[sup:2zetr3r8]2[/sup:2zetr3r8]+18x-36
x[sup:2zetr3r8]4[/sup:2zetr3r8]-8x[sup:2zetr3r8]3[/sup:2zetr3r8]+7x[sup:2zetr3r8]2[/sup:2zetr3r8]+36x+36

Is that right at all?

 

[BigGlenntheHeavy]

\(\displaystyle Correct \ answer \ is: \ x^4-8x^3+7x^2+36x-36 \ = \ (x-6)(x-3)(x-1)(x+2).\)

\(\displaystyle Here \ is \ its \ graph.\)

[attachment=0:z9mx02i7]mno.jpg[/attachment:z9mx02i7]