Mister Exam

# Factor polynomial x^3-x^2-x-2

An expression to simplify:

### The solution

You have entered [src]
 3    2
x  - x  - x - 2
$$\left(- x + \left(x^{3} - x^{2}\right)\right) - 2$$
x^3 - x^2 - x - 2
General simplification [src]
      3        2
-2 + x  - x - x 
$$x^{3} - x^{2} - x - 2$$
-2 + x^3 - x - x^2
Factorization [src]
        /            ___\ /            ___\
|    1   I*\/ 3 | |    1   I*\/ 3 |
(x - 2)*|x + - + -------|*|x + - - -------|
\    2      2   / \    2      2   /
$$\left(x - 2\right) \left(x + \left(\frac{1}{2} + \frac{\sqrt{3} i}{2}\right)\right) \left(x + \left(\frac{1}{2} - \frac{\sqrt{3} i}{2}\right)\right)$$
((x - 2)*(x + 1/2 + i*sqrt(3)/2))*(x + 1/2 - i*sqrt(3)/2)
Common denominator [src]
      3        2
-2 + x  - x - x 
$$x^{3} - x^{2} - x - 2$$
-2 + x^3 - x - x^2
Combining rational expressions [src]
-2 + x*(-1 + x*(-1 + x))
$$x \left(x \left(x - 1\right) - 1\right) - 2$$
-2 + x*(-1 + x*(-1 + x))
Trigonometric part [src]
      3        2
-2 + x  - x - x 
$$x^{3} - x^{2} - x - 2$$
-2 + x^3 - x - x^2
Powers [src]
      3        2
-2 + x  - x - x 
$$x^{3} - x^{2} - x - 2$$
-2 + x^3 - x - x^2
Combinatorics [src]
         /         2\
(-2 + x)*\1 + x + x /
$$\left(x - 2\right) \left(x^{2} + x + 1\right)$$
(-2 + x)*(1 + x + x^2)
Assemble expression [src]
      3        2
-2 + x  - x - x 
$$x^{3} - x^{2} - x - 2$$
-2 + x^3 - x - x^2
Rational denominator [src]
      3        2
-2 + x  - x - x 
$$x^{3} - x^{2} - x - 2$$
-2 + x^3 - x - x^2
-2.0 + x^3 - x - x^2
-2.0 + x^3 - x - x^2