Remainder

Algebra Level 3

If the polynomial P(x)=x9x6+x31 P(x)={ x }^{ 9 }-{ x }^{ 6 }+{ x }^{ 3 }-1 leaves r(x)r(x) as remainder when divided by d(x)=x2+x+1d(x)={ x }^{ 2 }+x+1, then, evaluate r(2015)r(2015).


Inspiration: Preparatory Classes to the Technological Institute of Aeronautics (ITA - Brazil).
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