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Expression simplification/ Factorization polynomials/ x^3+x-1

Factor polynomial x^3+x-1

An expression to simplify:

The solution

You have entered [src] 
 3        
x  + x - 1
$$\left(x^{3} + x\right) - 1$$ 
x^3 + x - 1
General simplification [src] 
          3
-1 + x + x
$$x^{3} + x - 1$$ 
-1 + x + x^3
Factorization [src] 
/           ____________                                                      \ /           ____________                                                      \ /           ____________                      \
|          /       ____  /          ___\                                      | |          /       ____  /          ___\                                      | |          /       ____                       |
|         /  1   \/ 93   |  1   I*\/ 3 |                    1                 | |         /  1   \/ 93   |  1   I*\/ 3 |                    1                 | |         /  1   \/ 93              1         |
|x + - 3 /   - + ------ *|- - - -------| + -----------------------------------|*|x + - 3 /   - + ------ *|- - + -------| + -----------------------------------|*|x + - 3 /   - + ------  + -------------------|
|      \/    2     18    \  2      2   /          ____________                | |      \/    2     18    \  2      2   /          ____________                | |      \/    2     18             ____________|
|                                                /       ____  /          ___\| |                                                /       ____  /          ___\| |                                /       ____ |
|                                               /  1   \/ 93   |  1   I*\/ 3 || |                                               /  1   \/ 93   |  1   I*\/ 3 || |                               /  1   \/ 93  |
|                                          3*3 /   - + ------ *|- - - -------|| |                                          3*3 /   - + ------ *|- - + -------|| |                          3*3 /   - + ------ |
\                                            \/    2     18    \  2      2   // \                                            \/    2     18    \  2      2   // \                            \/    2     18   /
$$\left(x + \left(\frac{1}{3 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{93}}{18}}} - \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{93}}{18}}\right)\right) \left(x + \left(- \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{93}}{18}} + \frac{1}{3 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1}{2} + \frac{\sqrt{93}}{18}}}\right)\right) \left(x + \left(- \sqrt[3]{\frac{1}{2} + \frac{\sqrt{93}}{18}} + \frac{1}{3 \sqrt[3]{\frac{1}{2} + \frac{\sqrt{93}}{18}}}\right)\right)$$ 
((x - (1/2 + sqrt(93)/18)^(1/3)*(-1/2 - i*sqrt(3)/2) + 1/(3*(1/2 + sqrt(93)/18)^(1/3)*(-1/2 - i*sqrt(3)/2)))*(x - (1/2 + sqrt(93)/18)^(1/3)*(-1/2 + i*sqrt(3)/2) + 1/(3*(1/2 + sqrt(93)/18)^(1/3)*(-1/2 + i*sqrt(3)/2))))*(x - (1/2 + sqrt(93)/18)^(1/3) + 1/(3*(1/2 + sqrt(93)/18)^(1/3)))
Combinatorics [src] 
          3
-1 + x + x
$$x^{3} + x - 1$$ 
-1 + x + x^3
Rational denominator [src] 
          3
-1 + x + x
$$x^{3} + x - 1$$ 
-1 + x + x^3
Powers [src] 
          3
-1 + x + x
$$x^{3} + x - 1$$ 
-1 + x + x^3
Numerical answer [src] 
-1.0 + x + x^3
-1.0 + x + x^3
Common denominator [src] 
          3
-1 + x + x
$$x^{3} + x - 1$$ 
-1 + x + x^3
Trigonometric part [src] 
          3
-1 + x + x
$$x^{3} + x - 1$$ 
-1 + x + x^3
Combining rational expressions [src] 
       /     2\
-1 + x*\1 + x /
$$x \left(x^{2} + 1\right) - 1$$ 
-1 + x*(1 + x^2)
Assemble expression [src] 
          3
-1 + x + x
$$x^{3} + x - 1$$ 
-1 + x + x^3
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