Question: Factorize:
$a^{2} x^{2}+\left(a x^{2}+1\right) x+a$
Solution:
We have:
$a^{2} x^{2}+\left(a x^{2}+1\right) x+a=\left(a x^{2}+1\right) x+\left(a^{2} x^{2}+a\right)$
$=x\left(a x^{2}+1\right)+a\left(a x^{2}+1\right)$
$=\left(a x^{2}+1\right)(x+a)$
