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प्रश्न
Factorize the following polynomial.
(x2 – x)2 – 8 (x2 – x) + 12
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उत्तर
(x2 – x)2 – 8 (x2 – x) + 12
Let x2 − x = z
∴ (x2 − x)2 − 8 (x2 − x) + 12
= z2 − 8z + 12
= z2 − 6z − 2z + 12
= z (z − 6) − 2 (z − 6)
= (z − 6)(z − 2)
= (x2 − x − 6) (x2 − x − 2) ...(Replace z = x2 − x)
= (x2 − 3x + 2x − 6) (x2 − 2x + x − 2)
= [x (x − 3) + 2 (x − 3)] [x (x − 2) + 1 (x − 2)]
= (x − 3) (x + 2) (x − 2) (x + 1)
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