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

(a x^{2} + 4) (a - x)

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(a x^{3} + 6) (a + x)

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

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(a x^{3} + 9) (a - x)

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Solution

The correct option is C $(a x^{2} + 1) (a + x)$
$a^{2} x^{2} + (a x^{2} + 1) x + a$
$= a^{2} x^{2} + a x^{3} + x + a$
$= a x^{2} (a + x) + (a + x)$
$= (x + a) (a x^{2} + 1)$

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