Question

Factorize the following polynomial.

 (y² + 5y) (y² + 5y – 2) – 24

Answer 1

(y² + 5y) (y² + 5y – 2) – 24

Let y² + 5y = z

∴ (y² + 5y) (y² + 5y – 2) – 24

= z (z – 2) – 24

= z² – 2z – 24

= z² – 6z + 4z – 24

= z (z – 6) + 4 (z – 6)

= (z – 6) (z + 4)

= (y² + 5y – 6) (y² + 5y + 4)   ...(Replace z = y² + 5y)

= (y² + 6y – y – 6) (y² + 4y + y + 4)

= [y (y + 6) – 1 (y + 6)] [y (y + 4) + 1 (y + 4)]

= (y + 6) (y – 1) (y + 4) (y + 1)