Mister Exam
Factor polynomial x+x^5/5+3*x^4/4
The solution
You have entered
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5 4
x 3*x
x + -- + ----
5 4
$$\frac{3 x^{4}}{4} + \left(\frac{x^{5}}{5} + x\right)$$
x + x^5/5 + (3*x^4)/4
General simplification
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5 4
x 3*x
x + -- + ----
5 4
$$\frac{x^{5}}{5} + \frac{3 x^{4}}{4} + x$$
x + x^5/5 + 3*x^4/4
Fraction decomposition
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x + x^5/5 + 3*x^4/4
$$\frac{x^{5}}{5} + \frac{3 x^{4}}{4} + x$$
5 4
x 3*x
x + -- + ----
5 4
Factorization
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$$x \left(x + \left(- \frac{\sqrt{\frac{10}{3 \sqrt[3]{\frac{5 \sqrt{3117585}}{2304} + \frac{1125}{256}}} + \frac{225}{64} + 2 \sqrt[3]{\frac{5 \sqrt{3117585}}{2304} + \frac{1125}{256}}}}{2} + \frac{15}{16} + \frac{\sqrt{- \frac{3375}{256 \sqrt{\frac{10}{3 \sqrt[3]{\frac{5 \sqrt{3117585}}{2304} + \frac{1125}{256}}} + \frac{225}{64} + 2 \sqrt[3]{\frac{5 \sqrt{3117585}}{2304} + \frac{1125}{256}}}} - 2 \sqrt[3]{\frac{5 \sqrt{3117585}}{2304} + \frac{1125}{256}} - \frac{10}{3 \sqrt[3]{\frac{5 \sqrt{3117585}}{2304} + \frac{1125}{256}}} + \frac{225}{32}}}{2}\right)\right) \left(x + \left(- \frac{\sqrt{\frac{10}{3 \sqrt[3]{\frac{5 \sqrt{3117585}}{2304} + \frac{1125}{256}}} + \frac{225}{64} + 2 \sqrt[3]{\frac{5 \sqrt{3117585}}{2304} + \frac{1125}{256}}}}{2} + \frac{15}{16} - \frac{\sqrt{- \frac{3375}{256 \sqrt{\frac{10}{3 \sqrt[3]{\frac{5 \sqrt{3117585}}{2304} + \frac{1125}{256}}} + \frac{225}{64} + 2 \sqrt[3]{\frac{5 \sqrt{3117585}}{2304} + \frac{1125}{256}}}} - 2 \sqrt[3]{\frac{5 \sqrt{3117585}}{2304} + \frac{1125}{256}} - \frac{10}{3 \sqrt[3]{\frac{5 \sqrt{3117585}}{2304} + \frac{1125}{256}}} + \frac{225}{32}}}{2}\right)\right) \left(x + \left(- \frac{\sqrt{- 2 \sqrt[3]{\frac{5 \sqrt{3117585}}{2304} + \frac{1125}{256}} - \frac{10}{3 \sqrt[3]{\frac{5 \sqrt{3117585}}{2304} + \frac{1125}{256}}} + \frac{3375}{256 \sqrt{\frac{10}{3 \sqrt[3]{\frac{5 \sqrt{3117585}}{2304} + \frac{1125}{256}}} + \frac{225}{64} + 2 \sqrt[3]{\frac{5 \sqrt{3117585}}{2304} + \frac{1125}{256}}}} + \frac{225}{32}}}{2} + \frac{15}{16} + \frac{\sqrt{\frac{10}{3 \sqrt[3]{\frac{5 \sqrt{3117585}}{2304} + \frac{1125}{256}}} + \frac{225}{64} + 2 \sqrt[3]{\frac{5 \sqrt{3117585}}{2304} + \frac{1125}{256}}}}{2}\right)\right) \left(x + \left(\frac{15}{16} + \frac{\sqrt{- 2 \sqrt[3]{\frac{5 \sqrt{3117585}}{2304} + \frac{1125}{256}} - \frac{10}{3 \sqrt[3]{\frac{5 \sqrt{3117585}}{2304} + \frac{1125}{256}}} + \frac{3375}{256 \sqrt{\frac{10}{3 \sqrt[3]{\frac{5 \sqrt{3117585}}{2304} + \frac{1125}{256}}} + \frac{225}{64} + 2 \sqrt[3]{\frac{5 \sqrt{3117585}}{2304} + \frac{1125}{256}}}} + \frac{225}{32}}}{2} + \frac{\sqrt{\frac{10}{3 \sqrt[3]{\frac{5 \sqrt{3117585}}{2304} + \frac{1125}{256}}} + \frac{225}{64} + 2 \sqrt[3]{\frac{5 \sqrt{3117585}}{2304} + \frac{1125}{256}}}}{2}\right)\right)$$
(((x*(x + 15/16 - sqrt(225/64 + 2*(1125/256 + 5*sqrt(3117585)/2304)^(1/3) + 10/(3*(1125/256 + 5*sqrt(3117585)/2304)^(1/3)))/2 + sqrt(225/32 - 2*(1125/256 + 5*sqrt(3117585)/2304)^(1/3) - 3375/(256*sqrt(225/64 + 2*(1125/256 + 5*sqrt(3117585)/2304)^(1/3) + 10/(3*(1125/256 + 5*sqrt(3117585)/2304)^(1/3)))) - 10/(3*(1125/256 + 5*sqrt(3117585)/2304)^(1/3)))/2))*(x + 15/16 - sqrt(225/64 + 2*(1125/256 + 5*sqrt(3117585)/2304)^(1/3) + 10/(3*(1125/256 + 5*sqrt(3117585)/2304)^(1/3)))/2 - sqrt(225/32 - 2*(1125/256 + 5*sqrt(3117585)/2304)^(1/3) - 3375/(256*sqrt(225/64 + 2*(1125/256 + 5*sqrt(3117585)/2304)^(1/3) + 10/(3*(1125/256 + 5*sqrt(3117585)/2304)^(1/3)))) - 10/(3*(1125/256 + 5*sqrt(3117585)/2304)^(1/3)))/2))*(x + 15/16 - sqrt(225/32 - 2*(1125/256 + 5*sqrt(3117585)/2304)^(1/3) - 10/(3*(1125/256 + 5*sqrt(3117585)/2304)^(1/3)) + 3375/(256*sqrt(225/64 + 2*(1125/256 + 5*sqrt(3117585)/2304)^(1/3) + 10/(3*(1125/256 + 5*sqrt(3117585)/2304)^(1/3)))))/2 + sqrt(225/64 + 2*(1125/256 + 5*sqrt(3117585)/2304)^(1/3) + 10/(3*(1125/256 + 5*sqrt(3117585)/2304)^(1/3)))/2))*(x + 15/16 + sqrt(225/64 + 2*(1125/256 + 5*sqrt(3117585)/2304)^(1/3) + 10/(3*(1125/256 + 5*sqrt(3117585)/2304)^(1/3)))/2 + sqrt(225/32 - 2*(1125/256 + 5*sqrt(3117585)/2304)^(1/3) - 10/(3*(1125/256 + 5*sqrt(3117585)/2304)^(1/3)) + 3375/(256*sqrt(225/64 + 2*(1125/256 + 5*sqrt(3117585)/2304)^(1/3) + 10/(3*(1125/256 + 5*sqrt(3117585)/2304)^(1/3)))))/2)
Powers
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5 4
x 3*x
x + -- + ----
5 4
$$\frac{x^{5}}{5} + \frac{3 x^{4}}{4} + x$$
x + x^5/5 + 3*x^4/4
Common denominator
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5 4
x 3*x
x + -- + ----
5 4
$$\frac{x^{5}}{5} + \frac{3 x^{4}}{4} + x$$
x + x^5/5 + 3*x^4/4
Assemble expression
[src]
5 4
x 3*x
x + -- + ----
5 4
$$\frac{x^{5}}{5} + \frac{3 x^{4}}{4} + x$$
x + x^5/5 + 3*x^4/4
Combinatorics
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/ 4 3\
x*\20 + 4*x + 15*x /
---------------------
20
$$\frac{x \left(4 x^{4} + 15 x^{3} + 20\right)}{20}$$
x*(20 + 4*x^4 + 15*x^3)/20
Rational denominator
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5 4
4*x + 15*x + 20*x
-------------------
20
$$\frac{4 x^{5} + 15 x^{4} + 20 x}{20}$$
(4*x^5 + 15*x^4 + 20*x)/20
Trigonometric part
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5 4
x 3*x
x + -- + ----
5 4
$$\frac{x^{5}}{5} + \frac{3 x^{4}}{4} + x$$
x + x^5/5 + 3*x^4/4
Combining rational expressions
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/ 4 3\
x*\20 + 4*x + 15*x /
---------------------
20
$$\frac{x \left(4 x^{4} + 15 x^{3} + 20\right)}{20}$$
x*(20 + 4*x^4 + 15*x^3)/20