Solve (x^14+x^13+1)div(x^2+x+1)

$$( { x }^{ 14 } + { x }^{ 13 } +1) \div ( { x }^{ 2 } +x+1)$$

Evaluate

$$\frac{x^{14}+x^{13}+1}{x^{2}+x+1}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\left(x^{2}+x+1\right)\left(x^{12}-x^{10}+x^{9}-x^{7}+x^{6}-x^{4}+x^{3}-x+1\right)}{x^{2}+x+1}$$

Cancel out x^{2}+x+1 in both numerator and denominator.

$$x^{12}-x^{10}+x^{9}-x^{7}+x^{6}-x^{4}+x^{3}-x+1$$

Expand

$$\frac{x^{14}+x^{13}+1}{x^{2}+x+1}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\left(x^{2}+x+1\right)\left(x^{12}-x^{10}+x^{9}-x^{7}+x^{6}-x^{4}+x^{3}-x+1\right)}{x^{2}+x+1}$$

Cancel out x^{2}+x+1 in both numerator and denominator.

$$x^{12}-x^{10}+x^{9}-x^{7}+x^{6}-x^{4}+x^{3}-x+1$$