Im a bit confussed with the way this function would be written..?

Question

The polynomial function with a degree of 5 with -2 as a zero of multiplcity of 3, 0 as zero of a multoplicity of 1, and 2 as a zero of multiplcity 1.
i know the answe is something like this, but im not 100% sure..

x^5 + 2x^4 - 4x^3 - 4x^2

does this look right ?

Answer 1

x(x - 2)(x + 2)^3 =
(x^2 - 2x)(x^3 + 6x^2 + 12x + 8) =

x^3(x^2 - 2x) + 6x^2(x^2 - 2x) + 12x(x^2 - 2x) + 8(x^2 - 2x) =

x^2x^3 - 2xx^3 + 6x^2x^2 - 12xx^2 + 12xx^2 - 24xx + 8x^2 - 16x =

x^5 - 2x^4 + 6x^4 - 12x^3 + 12x^3 - 24x^2 + 8x^2 - 16x =

x^5 + 4x^4 - 16x^2 - 16x

Answer 2

(x+2)^3(x)(x-2)
= (x^2+4x+4)(x^3-4x)
= x^5+4x^4-16x^2-16x
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Ideas to save time
Regroup: (x+2)^2(x)(x+2)(x-2) = (x^2+4x+4)(x^3-4x)
Rank the results from the highest degree to the lowest degree:
x^5 + 4x^4 + (4-4)x^3 - 16x^2 - 16x
The above two steps can be done with mental math. That's why I didn't write them out in my solution.
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I didn't expand (x+2)^3(x)(x-2) at first. Helmut posted his results ahead of me.