Given x^2+x-1=0, find the value of 2002x^3+2001x^2-2003x-2004

Given x^2+x-1=0, find the value of 2002x^3+2001x^2-2003x-2004

2002X^3+2001x^2-2003x-2004
=X (2002x2+2001x-2003)-2004
=X (2001x2+2001x-2001+x2-2)-2004
=X (x2-2)-2004
=X (1-x-2)-2004
=-X2-x-2004
=-1-2004
=-2005

Factorization: the third power of X - the square of X - X+1

=X (square-1 of X)-(square-1 of X)
=(X-1)(x-1)(x+1)