Question:
Factorize each of the following expression:
a2x2 + (ax2 + 1)x + a
Solution:
$a^{2} x^{2}+\left(a x^{2}+1\right) x+a=a^{2} x^{2}+a x^{3}+x+a$
$=\left(a x^{3}+a^{2} x^{2}\right)+(x+a)$ [Regrouping the expressions]
$=a x^{2}(x+a)+(x+a)$
$=\left(a x^{2}+1\right)(x+a)$ $[$ Taking $(x+a)$ as the common factor $]$
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