Answer
$(x^n-2)(3x^n-2)$
Work Step by Step
The product of the leading coefficient and the constant term is $3(4)=12$.
The factors of 12 whose sum is equal to the coefficient of the middle term (which is -8) are $-6$ and $-2$.
Rewrite the middle term using these factors to have:
$\\3x^{2n}-8x^n+4
\\=3x^{2n}-6x^n-2x^n+4
\\=(3x^{2n}-6x^n) + (-2x^n+4)$
Factor out the GCF of each group to have:
$\\=3x^n(x^n-2)+(-2)(x^n-2)$
Factor out the GCF of $x^n-2$ to have:
$\\=(x^n-2)(3x^n-2)$
