I remember dis, yey
so if a polynomial has roots [tex]r_1[/tex], [tex]r_2[/tex], [tex]r_3[/tex], it can be factored into
[tex]f(x)=a(x-r_1)^b(x-r_2)^c(x-r_3)^d[/tex] 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
[tex]P(x)=(x-4)(x-16)(x-(1+9i))(x-(1-9i))[/tex] which simplifies to
[tex]P(x)=(x-4)(x-16)(x-1-9i)(x-1+9i)[/tex] which expands to
[tex]P(x)=x^4-22x^3+186x^2-1768x+5248[/tex]
