Question

if p(x)=x^15-2004 x^14 + 2004 x^13-............-2004 x^2+2004 x,then find the value of p (2003)

Answer 1

Remainder Theorem we will use over here that will tell us that the value of P(2003),

2003 | 1 -2004 +2004 -2004 +2004 -2004 +2004 ...

         |    2003 -2003  2003 -2003  2003 -2003 ...

      ---------------------------------------------

            1    -1     1    -1     1    -1     1 ...

The remainder is 1 after division we perform with odd power & -1 after with  even power.  

last term is 1 so P(2003)=1