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Expression simplification/ Factorization polynomials/ x^4-15*x^2+12*x+5

Factor polynomial x^4-15*x^2+12*x+5

An expression to simplify:

The solution

You have entered [src] 
 4       2           
x  - 15*x  + 12*x + 5
$$\left(12 x + \left(x^{4} - 15 x^{2}\right)\right) + 5$$ 
x^4 - 15*x^2 + 12*x + 5
Factorization [src] 
/          ____\ /            ____\ /            ____\ /          ____\
|    3   \/ 29 | |      3   \/ 13 | |      3   \/ 13 | |    3   \/ 29 |
|x + - - ------|*|x + - - + ------|*|x + - - - ------|*|x + - + ------|
\    2     2   / \      2     2   / \      2     2   / \    2     2   /
$$\left(x + \left(- \frac{3}{2} + \frac{\sqrt{13}}{2}\right)\right) \left(x + \left(\frac{3}{2} - \frac{\sqrt{29}}{2}\right)\right) \left(x + \left(- \frac{\sqrt{13}}{2} - \frac{3}{2}\right)\right) \left(x + \left(\frac{3}{2} + \frac{\sqrt{29}}{2}\right)\right)$$ 
(((x + 3/2 - sqrt(29)/2)*(x - 3/2 + sqrt(13)/2))*(x - 3/2 - sqrt(13)/2))*(x + 3/2 + sqrt(29)/2)
General simplification [src] 
     4       2       
5 + x  - 15*x  + 12*x
$$x^{4} - 15 x^{2} + 12 x + 5$$ 
5 + x^4 - 15*x^2 + 12*x
Numerical answer [src] 
5.0 + x^4 + 12.0*x - 15.0*x^2
5.0 + x^4 + 12.0*x - 15.0*x^2
Assemble expression [src] 
     4       2       
5 + x  - 15*x  + 12*x
$$x^{4} - 15 x^{2} + 12 x + 5$$ 
5 + x^4 - 15*x^2 + 12*x
Trigonometric part [src] 
     4       2       
5 + x  - 15*x  + 12*x
$$x^{4} - 15 x^{2} + 12 x + 5$$ 
5 + x^4 - 15*x^2 + 12*x
Combining rational expressions [src] 
      /       /       2\\
5 + x*\12 + x*\-15 + x //
$$x \left(x \left(x^{2} - 15\right) + 12\right) + 5$$ 
5 + x*(12 + x*(-15 + x^2))
Powers [src] 
     4       2       
5 + x  - 15*x  + 12*x
$$x^{4} - 15 x^{2} + 12 x + 5$$ 
5 + x^4 - 15*x^2 + 12*x
Combinatorics [src] 
/      2      \ /      2      \
\-1 + x  - 3*x/*\-5 + x  + 3*x/
$$\left(x^{2} - 3 x - 1\right) \left(x^{2} + 3 x - 5\right)$$ 
(-1 + x^2 - 3*x)*(-5 + x^2 + 3*x)
Common denominator [src] 
     4       2       
5 + x  - 15*x  + 12*x
$$x^{4} - 15 x^{2} + 12 x + 5$$ 
5 + x^4 - 15*x^2 + 12*x
Rational denominator [src] 
     4       2       
5 + x  - 15*x  + 12*x
$$x^{4} - 15 x^{2} + 12 x + 5$$ 
5 + x^4 - 15*x^2 + 12*x
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