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प्रश्न
Factorize the following polynomial.
(y + 2) (y – 3) (y + 8) (y + 3) + 56
उत्तर
(y + 2) (y – 3) (y + 8) (y + 3) + 56
= (y + 2) (y + 3) (y + 8) (y – 3) + 56
= (y2 + 3y + 2y + 6) (y2 + 8y - 3y - 24) + 56
= (y2 + 5y + 6) (y2 + 5y – 24) + 56
Let y2 + 5y = z
∴ (y2 + 5y + 6) (y2 + 5y - 24) + 56
= (z + 6 ) (z - 24) + 56
= z2 - 24z + 6z - 144 + 56
= z2 - 18z - 144 + 56
= z2 - 18z - 88
= z2 - 22z + 4z - 88
= z (z - 22) + 4 (z - 22)
= (z - 22) (z + 4)
= (y2 + 5y - 22) (y2 + 5y + 4) ...(Replace z = y2 + 5y)
= (y2 + 5y - 22) (y2 + 4y + y + 4)
= (y2 + 5y - 22) [y (y + 4) + 1 ( y + 4)]
= (y2 + 5y - 22) (y + 4) (y + 1)
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