Answer
$(x^n+4)(x^n+2)$
Work Step by Step
Let
$u=x^n$
Then
$u^2=x^{2n}$
Thus, the given expression, in terms of $u$, is:
$=u^2+6u+8$
The leading coefficient of the trinomial is 1.
This means that the trinomial can be factored by looking for factors of the constant term $(8)$ whose sum is equal to the coefficient of the middle term $(6)$.
Note that:
$8 = 4(2)$ and $4+2=6$
This means that the factors we are looking for are 4 and 2.
Therefore the factors of the trinomial are: $u+4$ and $u+2$.
Thus,
$u^2+6u+8=(u+4)(u+2)$.
Change the expression in terms of $x$ to obtain:
$=(x^n+4)(x^n+2)$
