Mister Exam

Factor polynomial x^4+1

An expression to simplify:

The solution

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