Extreme Polynomial Division problem

Algebra Level 4

Find the remainder when \(x^{1001}-1\) is divided by \(x^4+x^3+2x^2+x+1\).

\[x^4-x^3\] \[-x^3+x^2 \] \[-x^4+x^3\] \[-x^2+x\] \[x^2-x\] \[-1+x\] \[x^3-x^2\] \[x+1\]