Write a polynomial function with rational coefficients so that p(x) = 0 has the given roots. 4, 16, and 1 + 9i

I remember dis, yey

so if a polynomial has roots , , , it can be factored into
where a,b,c,d are constants

also, if a polynomial has rational coefients and a+bi is a root, then a-bi must also be a root

so our roots we need are
4,16, 1+9i and 1-9i

so assuming multiplity 1 (that means we have something like [/tex]f(x)=a(x-r_1)^1(x-r_2)^1(x-r_3)^1[/tex])

we get that your function is
which simplifies to
which expands to