Mister Exam

Factor polynomial x^5+x

An expression to simplify:

The solution

You have entered [src]
 5    
x  + x
$$x^{5} + x$$
x^5 + x
Factorization [src]
  /      ___       ___\ /      ___       ___\ /        ___       ___\ /        ___       ___\
  |    \/ 2    I*\/ 2 | |    \/ 2    I*\/ 2 | |      \/ 2    I*\/ 2 | |      \/ 2    I*\/ 2 |
x*|x + ----- + -------|*|x + ----- - -------|*|x + - ----- + -------|*|x + - ----- - -------|
  \      2        2   / \      2        2   / \        2        2   / \        2        2   /
$$x \left(x + \left(\frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}\right)\right) \left(x + \left(\frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}\right)\right) \left(x + \left(- \frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}\right)\right) \left(x + \left(- \frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}\right)\right)$$
(((x*(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]
x + x^5
x + x^5
Combining rational expressions [src]
  /     4\
x*\1 + x /
$$x \left(x^{4} + 1\right)$$
x*(1 + x^4)
Combinatorics [src]
  /     4\
x*\1 + x /
$$x \left(x^{4} + 1\right)$$
x*(1 + x^4)