If P(x)=13x+11+3x+15n−1−3x+15n is a 5th degree polynomial, then value of n is 

If P(x)=13x+11+3x+15n13x+15n is a 5th degree polynomial, then value of n is 

  1. A

    9

  2. B

    11

  3. C

    23

  4. D

    21

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    Solution:

    P(x)=15na(1+a)n(1a)n
    where     a=3x+1
    Now,   P(x)=25na nC1a+nC3a3+ 
    Note that n must be odd, so that 3x+1 does not appear in P(x).
               P(x)=25n nC1+nC3a2++nCnan1                       =25n nC1+nC3(3x+1)+nC5(3x+1)2 ++nCn(3x+1)(n1)/2                        

    For this to be a polynomial of degree 5, n-12=5n=11.

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