Factorise: $a^{2} x^{2} + ({a x}^{2} + 1) x + a$

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Solution

$a^{2} x^{2} + (a x^{2} + 1) x + a$
$= a^{2} x^{2} + a x^{3} + x + a$
$= a x^{2} (a + x) + 1 (x + a)$
$= (x + a) (a x^{2} + 1)$

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