Mister Exam
Factor polynomial x^3-x^2-x-2
The solution
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3 2 x - x - x - 2
$$\left(- x + \left(x^{3} - x^{2}\right)\right) - 2$$
x^3 - x^2 - x - 2
Factorization
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/ ___\ / ___\
| 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)
Combining rational expressions
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-2 + x*(-1 + x*(-1 + x))
$$x \left(x \left(x - 1\right) - 1\right) - 2$$
-2 + x*(-1 + x*(-1 + x))
Combinatorics
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/ 2\ (-2 + x)*\1 + x + x /
$$\left(x - 2\right) \left(x^{2} + x + 1\right)$$
(-2 + x)*(1 + x + x^2)