Mister Exam

Other calculators

Expression simplification/ Factorization polynomials/ x^6-1

Factor polynomial x^6-1

An expression to simplify:

The solution

You have entered [src] 
 6    
x  - 1
$$x^{6} - 1$$ 
x^6 - 1
Factorization [src] 
                /            ___\ /            ___\ /              ___\ /              ___\
                |    1   I*\/ 3 | |    1   I*\/ 3 | |      1   I*\/ 3 | |      1   I*\/ 3 |
(x + 1)*(x - 1)*|x + - + -------|*|x + - - -------|*|x + - - + -------|*|x + - - - -------|
                \    2      2   / \    2      2   / \      2      2   / \      2      2   /
$$\left(x - 1\right) \left(x + 1\right) \left(x + \left(\frac{1}{2} + \frac{\sqrt{3} i}{2}\right)\right) \left(x + \left(\frac{1}{2} - \frac{\sqrt{3} i}{2}\right)\right) \left(x + \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right)\right) \left(x + \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right)\right)$$ 
(((((x + 1)*(x - 1))*(x + 1/2 + i*sqrt(3)/2))*(x + 1/2 - i*sqrt(3)/2))*(x - 1/2 + i*sqrt(3)/2))*(x - 1/2 - i*sqrt(3)/2)
Combinatorics [src] 
                 /         2\ /     2    \
(1 + x)*(-1 + x)*\1 + x + x /*\1 + x  - x/
$$\left(x - 1\right) \left(x + 1\right) \left(x^{2} - x + 1\right) \left(x^{2} + x + 1\right)$$ 
(1 + x)*(-1 + x)*(1 + x + x^2)*(1 + x^2 - x)
Numerical answer [src] 
-1.0 + x^6
-1.0 + x^6
    © Mister Exam – Calculator