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Question
Factorize the following polynomial.
(y2 + 5y) (y2 + 5y – 2) – 24
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Solution
(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)
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