Which polynomial function has a leading coefficient of 1, roots - 3 and 8 with multiplicity 1, and root 4 with multiplicity 2?

Is it multiple choice or short answer

It will be a polynomial of degree 4 because it has 4 roots.

written as factors it is

(x + 3) (x - 8) (x - 4) ^2

expanding:-

= (x^2 - 5x - 24) (x^2 - 8x + 16)

= x^4 - 8x^3 + 16x^2 - 5x^3 + 40x^2 - 80x - 24x^2 + 192x - 384

= x^4 - 13x^3 + 32x^2 + 112x - 384