We know that:
[tex]f(x)=(4x^3+20)^2[/tex][tex]g(x)=4x^3+20[/tex]and that:
[tex]f(x)=g(x)h(x)[/tex]pluggign the values we are given we get:
[tex]\begin{gathered} (4x^3+20)=(4x^3+20)h(x) \\ h(x)=\frac{(4x^3+20)^2}{4x^3+20} \\ h(x)=4x^3+20 \end{gathered}[/tex]Therefore:
[tex]h(x)=4x^3+20[/tex]