Set y=x^n; therefore,
[tex]\begin{gathered} y=x^n \\ \Rightarrow x^{2n}+10x^n+16=y^2+10y+16 \end{gathered}[/tex]
Thus,
[tex]\begin{gathered} y^2+10y+16=(y+8)(y+2) \\ \Rightarrow x^{2n}+10x^n+16=(y+8)(y+2)=(x^n+8)(x^n+2) \\ \Rightarrow x^{2n}+10x^n+16=(x^n+8)(x^n+2) \end{gathered}[/tex]
Then, the answer is (x^n+8)(x^n+2)
