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

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Solution

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

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

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

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