Question

what is a quartic polynomial function in standard form with zeros -2,4,4 and 3?

Answer 1

if you know the zeros (or roots) \(r_1,r_2,...,r_n\) of a polynomial \(P(x)\), you can write it in factored form as
\[P(x) = a(x-r_1)(x-r_2)...(x-r_n)\]where \(a\) is a constant of your choosing (often 1, for convenience). To put it in standard form, you just multiply that sucker out, and be glad that there are only 4 zeros here :-)