Factorize the following polynomials.

(x² – 2x + 3) (x² – 2x + 5) – 35

(x² – 2x + 3) (x² – 2x + 5) – 35

Put (x² – 2x) = a

⟹ (a + 3) (a + 5) – 35

⟹ (a² + 5a + 3a + 15) – 35

⟹ a² + 8a + 15 – 35

⟹ a² + 8a – 20

⟹ a² + 10a – 2a – 20

⟹ a (a + 10) – 2 (a + 10)

⟹ (a – 2) (a + 10)

⟹ But a = (x² – 2x)

⟹ (x² – 2x) + 10) ((x² – 2x) – 2)

⟹ (x² – 2x + 10) (x² – 2x – 2)

Therefore, the factorized form = (x² – 2x + 10) (x² – 2x – 2)