Mister Exam
Factor polynomial x-x^3/3+x^5/5+3*x^4/4
The solution
You have entered
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3 5 4
x x 3*x
x - -- + -- + ----
3 5 4
$$\frac{3 x^{4}}{4} + \left(\frac{x^{5}}{5} + \left(- \frac{x^{3}}{3} + x\right)\right)$$
x - x^3/3 + x^5/5 + (3*x^4)/4
General simplification
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3 5 4
x x 3*x
x - -- + -- + ----
3 5 4
$$\frac{x^{5}}{5} + \frac{3 x^{4}}{4} - \frac{x^{3}}{3} + x$$
x - x^3/3 + x^5/5 + 3*x^4/4
Fraction decomposition
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x - x^3/3 + x^5/5 + 3*x^4/4
$$\frac{x^{5}}{5} + \frac{3 x^{4}}{4} - \frac{x^{3}}{3} + x$$
3 5 4
x x 3*x
x - -- + -- + ----
3 5 4
Factorization
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/ _____________________________________________________________________________________________________________________________________________________________________________________\ / _____________________________________________________________________________________________________________________________________________________________________________________\ / _____________________________________________________________________________________________________________________________________________________________________________________ \ / _____________________________________________________________________________________________________________________________________________________________________________________\ | / ___________________________ | | / ___________________________ | | / ___________________________ | | / ___________________________ | | / / ___________ | | / / ___________ | | / / ___________ | | / / ___________ | | / 2665 / 1075325 5*\/ 479818785 4975 565 | | / 2665 / 1075325 5*\/ 479818785 4975 565 | | / 2665 / 1075325 5*\/ 479818785 565 4975 | | / 2665 / 1075325 5*\/ 479818785 565 4975 | | / ---- - 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-------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|x + -- - -------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|x + -- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------|*|x + -- + -------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| \ 16 2 2 / \ 16 2 2 / \ 16 2 2 / \ 16 2 2 /
$$x \left(x + \left(- \frac{\sqrt{\frac{565}{162 \sqrt[3]{\frac{5 \sqrt{479818785}}{20736} + \frac{1075325}{186624}}} + 2 \sqrt[3]{\frac{5 \sqrt{479818785}}{20736} + \frac{1075325}{186624}} + \frac{2665}{576}}}{2} + \frac{15}{16} + \frac{\sqrt{- \frac{4975}{256 \sqrt{\frac{565}{162 \sqrt[3]{\frac{5 \sqrt{479818785}}{20736} + \frac{1075325}{186624}}} + 2 \sqrt[3]{\frac{5 \sqrt{479818785}}{20736} + \frac{1075325}{186624}} + \frac{2665}{576}}} - 2 \sqrt[3]{\frac{5 \sqrt{479818785}}{20736} + \frac{1075325}{186624}} - \frac{565}{162 \sqrt[3]{\frac{5 \sqrt{479818785}}{20736} + \frac{1075325}{186624}}} + \frac{2665}{288}}}{2}\right)\right) \left(x + \left(- \frac{\sqrt{\frac{565}{162 \sqrt[3]{\frac{5 \sqrt{479818785}}{20736} + \frac{1075325}{186624}}} + 2 \sqrt[3]{\frac{5 \sqrt{479818785}}{20736} + \frac{1075325}{186624}} + \frac{2665}{576}}}{2} + \frac{15}{16} - \frac{\sqrt{- \frac{4975}{256 \sqrt{\frac{565}{162 \sqrt[3]{\frac{5 \sqrt{479818785}}{20736} + \frac{1075325}{186624}}} + 2 \sqrt[3]{\frac{5 \sqrt{479818785}}{20736} + \frac{1075325}{186624}} + \frac{2665}{576}}} - 2 \sqrt[3]{\frac{5 \sqrt{479818785}}{20736} + \frac{1075325}{186624}} - \frac{565}{162 \sqrt[3]{\frac{5 \sqrt{479818785}}{20736} + \frac{1075325}{186624}}} + \frac{2665}{288}}}{2}\right)\right) \left(x + \left(- \frac{\sqrt{- 2 \sqrt[3]{\frac{5 \sqrt{479818785}}{20736} + \frac{1075325}{186624}} - \frac{565}{162 \sqrt[3]{\frac{5 \sqrt{479818785}}{20736} + \frac{1075325}{186624}}} + \frac{4975}{256 \sqrt{\frac{565}{162 \sqrt[3]{\frac{5 \sqrt{479818785}}{20736} + \frac{1075325}{186624}}} + 2 \sqrt[3]{\frac{5 \sqrt{479818785}}{20736} + \frac{1075325}{186624}} + \frac{2665}{576}}} + \frac{2665}{288}}}{2} + \frac{15}{16} + \frac{\sqrt{\frac{565}{162 \sqrt[3]{\frac{5 \sqrt{479818785}}{20736} + \frac{1075325}{186624}}} + 2 \sqrt[3]{\frac{5 \sqrt{479818785}}{20736} + \frac{1075325}{186624}} + \frac{2665}{576}}}{2}\right)\right) \left(x + \left(\frac{15}{16} + \frac{\sqrt{- 2 \sqrt[3]{\frac{5 \sqrt{479818785}}{20736} + \frac{1075325}{186624}} - \frac{565}{162 \sqrt[3]{\frac{5 \sqrt{479818785}}{20736} + \frac{1075325}{186624}}} + \frac{4975}{256 \sqrt{\frac{565}{162 \sqrt[3]{\frac{5 \sqrt{479818785}}{20736} + \frac{1075325}{186624}}} + 2 \sqrt[3]{\frac{5 \sqrt{479818785}}{20736} + \frac{1075325}{186624}} + \frac{2665}{576}}} + \frac{2665}{288}}}{2} + \frac{\sqrt{\frac{565}{162 \sqrt[3]{\frac{5 \sqrt{479818785}}{20736} + \frac{1075325}{186624}}} + 2 \sqrt[3]{\frac{5 \sqrt{479818785}}{20736} + \frac{1075325}{186624}} + \frac{2665}{576}}}{2}\right)\right)$$
(((x*(x + 15/16 - sqrt(2665/576 + 2*(1075325/186624 + 5*sqrt(479818785)/20736)^(1/3) + 565/(162*(1075325/186624 + 5*sqrt(479818785)/20736)^(1/3)))/2 + sqrt(2665/288 - 2*(1075325/186624 + 5*sqrt(479818785)/20736)^(1/3) - 4975/(256*sqrt(2665/576 + 2*(1075325/186624 + 5*sqrt(479818785)/20736)^(1/3) + 565/(162*(1075325/186624 + 5*sqrt(479818785)/20736)^(1/3)))) - 565/(162*(1075325/186624 + 5*sqrt(479818785)/20736)^(1/3)))/2))*(x + 15/16 - sqrt(2665/576 + 2*(1075325/186624 + 5*sqrt(479818785)/20736)^(1/3) + 565/(162*(1075325/186624 + 5*sqrt(479818785)/20736)^(1/3)))/2 - sqrt(2665/288 - 2*(1075325/186624 + 5*sqrt(479818785)/20736)^(1/3) - 4975/(256*sqrt(2665/576 + 2*(1075325/186624 + 5*sqrt(479818785)/20736)^(1/3) + 565/(162*(1075325/186624 + 5*sqrt(479818785)/20736)^(1/3)))) - 565/(162*(1075325/186624 + 5*sqrt(479818785)/20736)^(1/3)))/2))*(x + 15/16 - sqrt(2665/288 - 2*(1075325/186624 + 5*sqrt(479818785)/20736)^(1/3) - 565/(162*(1075325/186624 + 5*sqrt(479818785)/20736)^(1/3)) + 4975/(256*sqrt(2665/576 + 2*(1075325/186624 + 5*sqrt(479818785)/20736)^(1/3) + 565/(162*(1075325/186624 + 5*sqrt(479818785)/20736)^(1/3)))))/2 + sqrt(2665/576 + 2*(1075325/186624 + 5*sqrt(479818785)/20736)^(1/3) + 565/(162*(1075325/186624 + 5*sqrt(479818785)/20736)^(1/3)))/2))*(x + 15/16 + sqrt(2665/576 + 2*(1075325/186624 + 5*sqrt(479818785)/20736)^(1/3) + 565/(162*(1075325/186624 + 5*sqrt(479818785)/20736)^(1/3)))/2 + sqrt(2665/288 - 2*(1075325/186624 + 5*sqrt(479818785)/20736)^(1/3) - 565/(162*(1075325/186624 + 5*sqrt(479818785)/20736)^(1/3)) + 4975/(256*sqrt(2665/576 + 2*(1075325/186624 + 5*sqrt(479818785)/20736)^(1/3) + 565/(162*(1075325/186624 + 5*sqrt(479818785)/20736)^(1/3)))))/2)
Rational denominator
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3 5 4
- 20*x + 12*x + 45*x + 60*x
------------------------------
60
$$\frac{12 x^{5} + 45 x^{4} - 20 x^{3} + 60 x}{60}$$
(-20*x^3 + 12*x^5 + 45*x^4 + 60*x)/60
Combining rational expressions
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/ 2 4 3\
x*\60 - 20*x + 12*x + 45*x /
------------------------------
60
$$\frac{x \left(12 x^{4} + 45 x^{3} - 20 x^{2} + 60\right)}{60}$$
x*(60 - 20*x^2 + 12*x^4 + 45*x^3)/60
Combinatorics
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/ 2 4 3\
x*\60 - 20*x + 12*x + 45*x /
------------------------------
60
$$\frac{x \left(12 x^{4} + 45 x^{3} - 20 x^{2} + 60\right)}{60}$$
x*(60 - 20*x^2 + 12*x^4 + 45*x^3)/60
Numerical answer
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x + 0.75*x^4 + 0.2*x^5 - 0.333333333333333*x^3
x + 0.75*x^4 + 0.2*x^5 - 0.333333333333333*x^3
Assemble expression
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3 5 4
x x 3*x
x - -- + -- + ----
3 5 4
$$\frac{x^{5}}{5} + \frac{3 x^{4}}{4} - \frac{x^{3}}{3} + x$$
x - x^3/3 + x^5/5 + 3*x^4/4
Common denominator
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3 5 4
x x 3*x
x - -- + -- + ----
3 5 4
$$\frac{x^{5}}{5} + \frac{3 x^{4}}{4} - \frac{x^{3}}{3} + x$$
x - x^3/3 + x^5/5 + 3*x^4/4
Trigonometric part
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3 5 4
x x 3*x
x - -- + -- + ----
3 5 4
$$\frac{x^{5}}{5} + \frac{3 x^{4}}{4} - \frac{x^{3}}{3} + x$$
x - x^3/3 + x^5/5 + 3*x^4/4
Powers
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3 5 4
x x 3*x
x - -- + -- + ----
3 5 4
$$\frac{x^{5}}{5} + \frac{3 x^{4}}{4} - \frac{x^{3}}{3} + x$$
x - x^3/3 + x^5/5 + 3*x^4/4