Mister Exam
Factor polynomial x-x^3+5*x^2/2
The solution
You have entered
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2
3 5*x
x - x + ----
2
$$\frac{5 x^{2}}{2} + \left(- x^{3} + x\right)$$
x - x^3 + (5*x^2)/2
Factorization
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/ ____\ / ____\ | 5 \/ 41 | | 5 \/ 41 | x*|x + - - + ------|*|x + - - - ------| \ 4 4 / \ 4 4 /
$$x \left(x + \left(- \frac{5}{4} + \frac{\sqrt{41}}{4}\right)\right) \left(x + \left(- \frac{\sqrt{41}}{4} - \frac{5}{4}\right)\right)$$
(x*(x - 5/4 + sqrt(41)/4))*(x - 5/4 - sqrt(41)/4)
Fraction decomposition
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x - x^3 + 5*x^2/2
$$- x^{3} + \frac{5 x^{2}}{2} + x$$
2
3 5*x
x - x + ----
2
General simplification
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/ 2 5*x\ x*|1 - x + ---| \ 2 /
$$x \left(- x^{2} + \frac{5 x}{2} + 1\right)$$
x*(1 - x^2 + 5*x/2)
Combining rational expressions
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/ 2 \
x*\2 - 2*x + 5*x/
------------------
2
$$\frac{x \left(- 2 x^{2} + 5 x + 2\right)}{2}$$
x*(2 - 2*x^2 + 5*x)/2
Common denominator
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2
3 5*x
x - x + ----
2
$$- x^{3} + \frac{5 x^{2}}{2} + x$$
x - x^3 + 5*x^2/2
Trigonometric part
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2
3 5*x
x - x + ----
2
$$- x^{3} + \frac{5 x^{2}}{2} + x$$
x - x^3 + 5*x^2/2
Combinatorics
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/ 2\
-x*\-2 - 5*x + 2*x /
---------------------
2
$$- \frac{x \left(2 x^{2} - 5 x - 2\right)}{2}$$
-x*(-2 - 5*x + 2*x^2)/2
Assemble expression
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2
3 5*x
x - x + ----
2
$$- x^{3} + \frac{5 x^{2}}{2} + x$$
x - x^3 + 5*x^2/2
Rational denominator
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3 2
- 2*x + 2*x + 5*x
-------------------
2
$$\frac{- 2 x^{3} + 5 x^{2} + 2 x}{2}$$
(-2*x^3 + 2*x + 5*x^2)/2