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Let P(x)=x^4+a x^3+b x^2+c x+d be a poly...

Let `P(x)=x^4+a x^3+b x^2+c x+d` be a polynomial such that `P(1)=1,P(2)=8,+P(3)=27 ,P(4)=64` then the value of `152-P(5)` is____________.

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The correct Answer is:
149
Cleraly, `P(x)-x^(3)=0` has roots 1, 2, 3, 4.
`:.P(x)-x^(3)=(x-1)(x-2)(x-3)(x-4)`
`impliesP(x)=(x-1)(x-2)(x-3)(x-4)+x^(3)`
Hence, `P(5)=1xx2xx3xx4+125=149`
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