Mister Exam

# Factor polynomial x^8-1

An expression to simplify:

### The solution

You have entered [src]
 8
x  - 1
$$x^{8} - 1$$
x^8 - 1
Factorization [src]
                                /      ___       ___\ /      ___       ___\ /        ___       ___\ /        ___       ___\
|    \/ 2    I*\/ 2 | |    \/ 2    I*\/ 2 | |      \/ 2    I*\/ 2 | |      \/ 2    I*\/ 2 |
(x + 1)*(x - 1)*(x + I)*(x - I)*|x + ----- + -------|*|x + ----- - -------|*|x + - ----- + -------|*|x + - ----- - -------|
\      2        2   / \      2        2   / \        2        2   / \        2        2   /
$$\left(x - 1\right) \left(x + 1\right) \left(x + i\right) \left(x - i\right) \left(x + \left(\frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}\right)\right) \left(x + \left(\frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}\right)\right) \left(x + \left(- \frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}\right)\right) \left(x + \left(- \frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}\right)\right)$$
(((((((x + 1)*(x - 1))*(x + i))*(x - i))*(x + sqrt(2)/2 + i*sqrt(2)/2))*(x + sqrt(2)/2 - i*sqrt(2)/2))*(x - sqrt(2)/2 + i*sqrt(2)/2))*(x - sqrt(2)/2 - i*sqrt(2)/2)
Combinatorics [src]
        /     2\ /     4\
(1 + x)*\1 + x /*\1 + x /*(-1 + x)
$$\left(x - 1\right) \left(x + 1\right) \left(x^{2} + 1\right) \left(x^{4} + 1\right)$$
(1 + x)*(1 + x^2)*(1 + x^4)*(-1 + x)
-1.0 + x^8
-1.0 + x^8