Wir haben folgendes:
a) $$x^3+2x^2+2x+1=x^3+x^2+x^2+x+x+1 \\ =x^3+x^2+x+x^2+x+1 \\ =x\left(x^2+x+1\right)+x^2+x+1 \\ =\left(x^2+x+1\right)\left(x+1\right)$$
b) $$x^{10}+x^8+x^6+x^4+x^2+1=x^2\cdot x^8+x^8+x^2\cdot x^4+x^4+x^2+1 \\ =x^8\left(x^2+1\right)+x^4\left(x^2+1\right)+x^2+1 \\ =\left(x^2+1\right)\left(x^8+x^4+x^2+1\right)$$