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Question
Factorize the following polynomial.
(x – 3) (x – 4)2 (x – 5) – 6
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Solution
(x – 3) (x – 4)2 (x – 5) – 6
= (x – 3)(x – 5) (x – 4)2 – 6
= (x2 – 8x + 15) (x2 – 8x + 16) – 6
Let x2 – 8x = z
∴ (x2 − 8x + 15) (x2 − 8x + 16) − 6
= (z + 15) (z + 16) − 6
= z2 + 31z + 240 − 6
= z2 + 31z + 234
= z2 + 18z + 13z + 234
= z(z + 18) 13(z + 18)
= (z + 18) (z + 13)
= (x2 − 8x + 18) (x2 − 8x + 13) ...(Replace z = x2 − 8x)
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