Prove that $x^n-a^n$ is divisible by $x+a$ only when $n$ is even.

Divide $p\left(x\right)$ by $d\left(x\right)$ and then verify division algorithm.

$p\left(x\right)=2x^3+x^2-x \text{and} d\left(x\right)=x$

Divide $p\left(x\right)$ by $d\left(x\right)$ and then verify division algorithm.

$p\left(x\right)=3x^2-x-1 \text{and} d\left(x\right)=-x$

Divide $p\left(x\right)$ by $d\left(x\right)$ and then verify division algorithm.

$p\left(x\right)=3x^2+2x+1 \text{and} d\left(x\right)=x+1$

Divide $p\left(x\right)$ by $d\left(x\right)$ and then verify division algorithm.

$p\left(x\right)=x^3-1 \text{and} d\left(x\right)=x-1$

Divide $p\left(x\right)$ by $d\left(x\right)$ and then verify division algorithm.

$p\left(x\right)=2x^2+3x+1 \text{and} d\left(x\right)=2+x$

Divide $p\left(x\right)$ by $d\left(x\right)$ and then verify division algorithm.

$p\left(x\right)=x^3-3x^2+5x-3 \text{and} d\left(x\right)=x^2-2$

Divide $p\left(x\right)$ by $d\left(x\right)$ and then verify division algorithm.

$p\left(x\right)=4x^3+4x^2-x+1 \text{and} d\left(x\right)=x^2+2x$

Divide $p\left(x\right)$ by $d\left(x\right)$ and then verify division algorithm.

$p\left(x\right)=3x^2-x^3-3x+5 \text{and} d\left(x\right)=x-1-x^2$