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

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Solution

a² x² + (ax² + 1)x + a

a² x² + (ax² + 1)x + a

= a² x² + ax³ + x + a

= ax² (a + x) + 1 (x + a)

= (ax² + 1) (a + x)

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