Without expanding, find the remainder when $x^{100} + 1$ is divided by $x^2 + x + 1$. Hint:

Question

Without expanding, find the remainder when $x^{100} + 1$ is divided by $x^2 + x + 1$. Hint: use $x^3-1=(x-1)(x^2+x+1)$ to reduce powers modulo the divisor.

Accepted Answer

$x+1$

Polynomials, Cubic Equations and Partial Fractions - Polynomial Division and Remainders

Polynomials, Cubic Equations and Partial Fractions - Polynomial Division and Remainders

Solution:

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