Factorize:$ a^{2} x^{2}+\left(a x^{2}+1\right) x+a $

Given :

\( a^{2} x^{2}+\left(a x^{2}+1\right) x+a \)

To do :

We have to factorize the given expression.

Solution :

$a^2x^2 + (ax^2 + 1)x + a = a^2x^2 + a + (ax^2 + 1)x$

$= a(ax^2 + 1) + x(ax^2 + 1)$

$= (ax^2 + 1) (a + x)$

$= (x + a) (ax^2 + 1)$

Hence, $a^2x^2 + (ax^2 + 1)x + a = (x + a) (ax^2 + 1)$.

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Updated on: 10-Oct-2022

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