Mister Exam
Factor polynomial x+x^2/2+4*x^3/3
The solution
You have entered
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2 3
x 4*x
x + -- + ----
2 3
$$\frac{4 x^{3}}{3} + \left(\frac{x^{2}}{2} + x\right)$$
x + x^2/2 + (4*x^3)/3
Fraction decomposition
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x + x^2/2 + 4*x^3/3
$$\frac{4 x^{3}}{3} + \frac{x^{2}}{2} + x$$
2 3
x 4*x
x + -- + ----
2 3
Factorization
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/ _____\ / _____\ | 3 I*\/ 183 | | 3 I*\/ 183 | x*|x + -- + ---------|*|x + -- - ---------| \ 16 16 / \ 16 16 /
$$x \left(x + \left(\frac{3}{16} + \frac{\sqrt{183} i}{16}\right)\right) \left(x + \left(\frac{3}{16} - \frac{\sqrt{183} i}{16}\right)\right)$$
(x*(x + 3/16 + i*sqrt(183)/16))*(x + 3/16 - i*sqrt(183)/16)
General simplification
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/ 2\
x*\6 + 3*x + 8*x /
------------------
6
$$\frac{x \left(8 x^{2} + 3 x + 6\right)}{6}$$
x*(6 + 3*x + 8*x^2)/6
Trigonometric part
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2 3
x 4*x
x + -- + ----
2 3
$$\frac{4 x^{3}}{3} + \frac{x^{2}}{2} + x$$
x + x^2/2 + 4*x^3/3
Common denominator
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2 3
x 4*x
x + -- + ----
2 3
$$\frac{4 x^{3}}{3} + \frac{x^{2}}{2} + x$$
x + x^2/2 + 4*x^3/3
Rational denominator
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2 3
3*x + 6*x + 8*x
-----------------
6
$$\frac{8 x^{3} + 3 x^{2} + 6 x}{6}$$
(3*x^2 + 6*x + 8*x^3)/6
Assemble expression
[src]
2 3
x 4*x
x + -- + ----
2 3
$$\frac{4 x^{3}}{3} + \frac{x^{2}}{2} + x$$
x + x^2/2 + 4*x^3/3
Combining rational expressions
[src]
/ 2\
x*\6 + 3*x + 8*x /
------------------
6
$$\frac{x \left(8 x^{2} + 3 x + 6\right)}{6}$$
x*(6 + 3*x + 8*x^2)/6
Powers
[src]
2 3
x 4*x
x + -- + ----
2 3
$$\frac{4 x^{3}}{3} + \frac{x^{2}}{2} + x$$
x + x^2/2 + 4*x^3/3
Combinatorics
[src]
/ 2\
x*\6 + 3*x + 8*x /
------------------
6
$$\frac{x \left(8 x^{2} + 3 x + 6\right)}{6}$$
x*(6 + 3*x + 8*x^2)/6