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Expression simplification/ Factorization polynomials/ x-x^3+3*x^2

Factor polynomial x-x^3+3*x^2

An expression to simplify:

The solution

You have entered [src] 
     3      2
x - x  + 3*x
$$3 x^{2} + \left(- x^{3} + x\right)$$ 
x - x^3 + 3*x^2
Factorization [src] 
  /            ____\ /            ____\
  |      3   \/ 13 | |      3   \/ 13 |
x*|x + - - + ------|*|x + - - - ------|
  \      2     2   / \      2     2   /
$$x \left(x + \left(- \frac{3}{2} + \frac{\sqrt{13}}{2}\right)\right) \left(x + \left(- \frac{\sqrt{13}}{2} - \frac{3}{2}\right)\right)$$ 
(x*(x - 3/2 + sqrt(13)/2))*(x - 3/2 - sqrt(13)/2)
General simplification [src] 
  /     2      \
x*\1 - x  + 3*x/
$$x \left(- x^{2} + 3 x + 1\right)$$ 
x*(1 - x^2 + 3*x)
Common denominator [src] 
     3      2
x - x  + 3*x
$$- x^{3} + 3 x^{2} + x$$ 
x - x^3 + 3*x^2
Numerical answer [src] 
x - x^3 + 3.0*x^2
x - x^3 + 3.0*x^2
Rational denominator [src] 
     3      2
x - x  + 3*x
$$- x^{3} + 3 x^{2} + x$$ 
x - x^3 + 3*x^2
Combining rational expressions [src] 
  /     2      \
x*\1 - x  + 3*x/
$$x \left(- x^{2} + 3 x + 1\right)$$ 
x*(1 - x^2 + 3*x)
Combinatorics [src] 
   /      2      \
-x*\-1 + x  - 3*x/
$$- x \left(x^{2} - 3 x - 1\right)$$ 
-x*(-1 + x^2 - 3*x)
Trigonometric part [src] 
     3      2
x - x  + 3*x
$$- x^{3} + 3 x^{2} + x$$ 
x - x^3 + 3*x^2
Powers [src] 
     3      2
x - x  + 3*x
$$- x^{3} + 3 x^{2} + x$$ 
x - x^3 + 3*x^2
Assemble expression [src] 
     3      2
x - x  + 3*x
$$- x^{3} + 3 x^{2} + x$$ 
x - x^3 + 3*x^2
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