Factorize:

ax³ – bx² + ax – b

Given ax³ – bx² + ax – b = (x² × ax – x² × b + ax – b)

Taking x² common from 1^st and 2^nd term and 1 from 3^rd and 4^th,

ax³ – bx² + ax – b = (x² × ax – x² × b + ax – b)

⇒ ax³ – bx² + ax – b = x² (ax – b) + (ax – b)

⇒ ax³ – bx² + ax – b = (x² + 1)(ax – b)