Factorize the following polynomials.

(x – 3) (x- 5) (x – 4)² – 6

(x – 3) (x- 5) (x – 4)² – 6

⟹ (x² – 8x + 15) (x² – 8x + 16) – 6

⟹ Put (x² – 8x) = a

⟹ (a + 15) (a + 16) – 6

⟹ a² + 15a + 16a + 240 – 6

⟹ a² + 31a + 234

⟹ a² + 13a + 18a + 234

⟹ a (a + 13) + 18 (a + 13)

⟹ (a + 18) (a + 13)

⟹ But a = (x² – 8x)

⟹ ((x² – 8x) + 18) ((x² – 8x) + 13)

⟹ (x² – 8x + 18) (x² – 8x + 13)

Therefore, the factorized form =(x² – 8x + 18) (x² – 8x + 13)