Factorize:
$a x^{3} - b x^{2} + a x - b$

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Solution

Given polynomial is $a x^{3} - b x^{2} + a x - b$
It can be factorised as
$a x^{3} - b x^{2} + a x - b = x^{2} (a x - b) + 1 (a x - b)$
$= (a x - b) (x^{2} + 1)$
Thus factors are $(a x - b), (x^{2} + 1)$ .

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