Find the polynomial function with the given zeros?

Where you write 4(x^2-4x+13)(x-3), the answer to that alone is 4x^3-28x^2+100x-156 and when you multiply in x^3, the answer would be 4x^6-28x^5+100x^4-156x^3. So you set it up write, but it's the numbers you somewhere got wrong. Looking at your first distribution I can see that when you multiplied the -3 to the -4x, you put in +4x instead of 12x. I do this all the time and I hate it when I know I messed up, especially when it comes down to the bare basics, but hey, it happens to us all at some point. Hope this helped!

notice x = 0 is a triple root, so u should start with:

x^3(x - a)(x - b)(x - c) = 0

ignore the leading coefficient for now.

actually, the other 3 roots were given :) nice!

a = 3

b = 2 - 3i

c = 2 + 3i

i would start with expanding

(x - 2 + 3i)(x - 2 - 3i)

(x - 2)^2 + 9

x^2 - 4x + 13

multiply this by (x - 3)

x^3 - 4x^2 + 13x

- 3x^2 + 12x - 39

x^3 - 7x^2 + 25x - 39

then multiply by the tripple root x = 0

x^6 - 7x^5 + 25x^4 - 39x^3

now we need the leading coefficient to be 4

4x^6 - 28x^5 + 100x^4 - 156x^3