Mister Exam
Factor polynomial z^3-z^2-2*z/5+8/125
The solution
You have entered
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3 2 2*z 8
z - z - --- + ---
5 125
$$\left(- \frac{2 z}{5} + \left(z^{3} - z^{2}\right)\right) + \frac{8}{125}$$
z^3 - z^2 - 2*z/5 + 8/125
General simplification
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8 3 2 2*z --- + z - z - --- 125 5
$$z^{3} - z^{2} - \frac{2 z}{5} + \frac{8}{125}$$
8/125 + z^3 - z^2 - 2*z/5
Fraction decomposition
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8/125 + z^3 - z^2 - 2*z/5
$$z^{3} - z^{2} - \frac{2 z}{5} + \frac{8}{125}$$
8 3 2 2*z --- + z - z - --- 125 5
Factorization
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/ ____\ / ____\
| 7 \/ 33 | | 7 \/ 33 |
(x + 2/5)*|x + - -- + ------|*|x + - -- - ------|
\ 10 10 / \ 10 10 /
$$\left(x + \frac{2}{5}\right) \left(x + \left(- \frac{7}{10} + \frac{\sqrt{33}}{10}\right)\right) \left(x + \left(- \frac{7}{10} - \frac{\sqrt{33}}{10}\right)\right)$$
((x + 2/5)*(x - 7/10 + sqrt(33)/10))*(x - 7/10 - sqrt(33)/10)
Rational denominator
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2 3
40 - 625*z - 250*z + 625*z
----------------------------
625
$$\frac{625 z^{3} - 625 z^{2} - 250 z + 40}{625}$$
(40 - 625*z^2 - 250*z + 625*z^3)/625
Powers
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8 3 2 2*z --- + z - z - --- 125 5
$$z^{3} - z^{2} - \frac{2 z}{5} + \frac{8}{125}$$
8/125 + z^3 - z^2 - 2*z/5
Common denominator
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8 3 2 2*z --- + z - z - --- 125 5
$$z^{3} - z^{2} - \frac{2 z}{5} + \frac{8}{125}$$
8/125 + z^3 - z^2 - 2*z/5
Combinatorics
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/ 2\
(2 + 5*z)*\4 - 35*z + 25*z /
----------------------------
125
$$\frac{\left(5 z + 2\right) \left(25 z^{2} - 35 z + 4\right)}{125}$$
(2 + 5*z)*(4 - 35*z + 25*z^2)/125
Assemble expression
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8 3 2 2*z --- + z - z - --- 125 5
$$z^{3} - z^{2} - \frac{2 z}{5} + \frac{8}{125}$$
8/125 + z^3 - z^2 - 2*z/5
Trigonometric part
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8 3 2 2*z --- + z - z - --- 125 5
$$z^{3} - z^{2} - \frac{2 z}{5} + \frac{8}{125}$$
8/125 + z^3 - z^2 - 2*z/5
Combining rational expressions
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8 + 25*z*(-2 + 5*z*(-1 + z))
----------------------------
125
$$\frac{25 z \left(5 z \left(z - 1\right) - 2\right) + 8}{125}$$
(8 + 25*z*(-2 + 5*z*(-1 + z)))/125