Factorize the following polynomials.

(x² – x)² – 8(x² – x) + 12

Put (x² – x) = a

⟹ a² – 8a + 12

⟹ a² – 2a – 6a + 12

⟹ a (a-2) – 6(a-2)

⟹ (a-6) × (a-2)

⟹ but a = (x² – x)

⟹ ((x² – x)-6) × ((x² – x) – 2

⟹ (x² – x -6) × (x² – x -2)

⟹ (x² –3x + 2x – 6) × (x² – 2x + x -2)

⟹ (x (x-3) + 2(x – 3)) × (x(x-2) + 1(x-2))

⟹ (x + 2)(x-3)(x-2)(x+1)

Therefore, the factorized form = (x + 2)(x-3)(x-2)(x+1)