Mister Exam
Factor polynomial s^3+61*s^2/100+51*s/500
The solution
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2
3 61*s 51*s
s + ----- + ----
100 500
$$\frac{51 s}{500} + \left(s^{3} + \frac{61 s^{2}}{100}\right)$$
s^3 + (61*s^2)/100 + (51*s)/500
General simplification
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/ 2\
s*\51 + 305*s + 500*s /
-----------------------
500
$$\frac{s \left(500 s^{2} + 305 s + 51\right)}{500}$$
s*(51 + 305*s + 500*s^2)/500
Fraction decomposition
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s^3 + 51*s/500 + 61*s^2/100
$$s^{3} + \frac{61 s^{2}}{100} + \frac{51 s}{500}$$
2
3 51*s 61*s
s + ---- + -----
500 100
Factorization
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/ _____\ / _____\ | 61 I*\/ 359 | | 61 I*\/ 359 | s*|s + --- + ---------|*|s + --- - ---------| \ 200 200 / \ 200 200 /
$$s \left(s + \left(\frac{61}{200} + \frac{\sqrt{359} i}{200}\right)\right) \left(s + \left(\frac{61}{200} - \frac{\sqrt{359} i}{200}\right)\right)$$
(s*(s + 61/200 + i*sqrt(359)/200))*(s + 61/200 - i*sqrt(359)/200)
Trigonometric part
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2
3 51*s 61*s
s + ---- + -----
500 100
$$s^{3} + \frac{61 s^{2}}{100} + \frac{51 s}{500}$$
s^3 + 51*s/500 + 61*s^2/100
Combining rational expressions
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s*(51 + 5*s*(61 + 100*s))
-------------------------
500
$$\frac{s \left(5 s \left(100 s + 61\right) + 51\right)}{500}$$
s*(51 + 5*s*(61 + 100*s))/500
Powers
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2
3 51*s 61*s
s + ---- + -----
500 100
$$s^{3} + \frac{61 s^{2}}{100} + \frac{51 s}{500}$$
s^3 + 51*s/500 + 61*s^2/100
Assemble expression
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2
3 51*s 61*s
s + ---- + -----
500 100
$$s^{3} + \frac{61 s^{2}}{100} + \frac{51 s}{500}$$
s^3 + 51*s/500 + 61*s^2/100
Rational denominator
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2 3
5100*s + 30500*s + 50000*s
----------------------------
50000
$$\frac{50000 s^{3} + 30500 s^{2} + 5100 s}{50000}$$
(5100*s + 30500*s^2 + 50000*s^3)/50000
Combinatorics
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/ 2\
s*\51 + 305*s + 500*s /
-----------------------
500
$$\frac{s \left(500 s^{2} + 305 s + 51\right)}{500}$$
s*(51 + 305*s + 500*s^2)/500
Common denominator
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2
3 51*s 61*s
s + ---- + -----
500 100
$$s^{3} + \frac{61 s^{2}}{100} + \frac{51 s}{500}$$
s^3 + 51*s/500 + 61*s^2/100