Factorize the following polynomials.

(y² + 5y)(y² + 5y – 2) - 24

Put (y² + 5y) = a

⟹ a (a -2) – 24

⟹ a² -2a – 24

⟹ a² -6a + 4a – 24

⟹ a (a – 6) + 4 (a – 6)

⟹ (a + 4) (a – 6)

⟹ But a = (y² + 5y)

⟹ ((y² + 5y) + 4) ((y² + 5y) – 6)

⟹ (y² + 5y + 4) (y² + 5y – 6)

⟹ (y² + 4y + y + 4) (y² + 6y - y – 6)

⟹ (y (y + 4) + 1 (y + 4)) (y (y + 6) – 1 (y + 6))

⟹ (y + 4) (y + 1) (y + 6) (y – 1)

Therefore, the factorized form = (y + 4) (y + 1) (y + 6) (y – 1)