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Expression simplification/ Factorization polynomials/ x^5+2*x^3+2*x^2+1

Factor polynomial x^5+2*x^3+2*x^2+1

An expression to simplify:

The solution

You have entered [src] 
 5      3      2    
x  + 2*x  + 2*x  + 1
$$\left(2 x^{2} + \left(x^{5} + 2 x^{3}\right)\right) + 1$$ 
x^5 + 2*x^3 + 2*x^2 + 1
General simplification [src] 
     5      2      3
1 + x  + 2*x  + 2*x
$$x^{5} + 2 x^{3} + 2 x^{2} + 1$$ 
1 + x^5 + 2*x^2 + 2*x^3
Factorization [src] 
        /                             ______________\ /                   ______________          \ /                             ______________\ /                             ______________\
        |              ___     ___   /          ___ | |            ___   /          ___        ___| |              ___     ___   /          ___ | |              ___     ___   /          ___ |
        |      1   I*\/ 3    \/ 2 *\/  -9 - I*\/ 3  | |      1   \/ 2 *\/  -9 + I*\/ 3     I*\/ 3 | |      1   I*\/ 3    \/ 2 *\/  -9 - I*\/ 3  | |      1   I*\/ 3    \/ 2 *\/  -9 + I*\/ 3  |
(x + 1)*|x + - - + ------- - -----------------------|*|x + - - + ----------------------- - -------|*|x + - - + ------- + -----------------------|*|x + - - - ------- - -----------------------|
        \      4      4                 4           / \      4              4                 4   / \      4      4                 4           / \      4      4                 4           /
$$\left(x + 1\right) \left(x + \left(- \frac{1}{4} + \frac{\sqrt{3} i}{4} - \frac{\sqrt{2} \sqrt{-9 - \sqrt{3} i}}{4}\right)\right) \left(x + \left(- \frac{1}{4} - \frac{\sqrt{3} i}{4} + \frac{\sqrt{2} \sqrt{-9 + \sqrt{3} i}}{4}\right)\right) \left(x + \left(- \frac{1}{4} + \frac{\sqrt{2} \sqrt{-9 - \sqrt{3} i}}{4} + \frac{\sqrt{3} i}{4}\right)\right) \left(x + \left(- \frac{1}{4} - \frac{\sqrt{2} \sqrt{-9 + \sqrt{3} i}}{4} - \frac{\sqrt{3} i}{4}\right)\right)$$ 
((((x + 1)*(x - 1/4 + i*sqrt(3)/4 - sqrt(2)*sqrt(-9 - i*sqrt(3))/4))*(x - 1/4 + sqrt(2)*sqrt(-9 + i*sqrt(3))/4 - i*sqrt(3)/4))*(x - 1/4 + i*sqrt(3)/4 + sqrt(2)*sqrt(-9 - i*sqrt(3))/4))*(x - 1/4 - i*sqrt(3)/4 - sqrt(2)*sqrt(-9 + i*sqrt(3))/4)
Assemble expression [src] 
     5      2      3
1 + x  + 2*x  + 2*x
$$x^{5} + 2 x^{3} + 2 x^{2} + 1$$ 
1 + x^5 + 2*x^2 + 2*x^3
Trigonometric part [src] 
     5      2      3
1 + x  + 2*x  + 2*x
$$x^{5} + 2 x^{3} + 2 x^{2} + 1$$ 
1 + x^5 + 2*x^2 + 2*x^3
Common denominator [src] 
     5      2      3
1 + x  + 2*x  + 2*x
$$x^{5} + 2 x^{3} + 2 x^{2} + 1$$ 
1 + x^5 + 2*x^2 + 2*x^3
Combining rational expressions [src] 
     2 /      /     2\\
1 + x *\2 + x*\2 + x //
$$x^{2} \left(x \left(x^{2} + 2\right) + 2\right) + 1$$ 
1 + x^2*(2 + x*(2 + x^2))
Rational denominator [src] 
     5      2      3
1 + x  + 2*x  + 2*x
$$x^{5} + 2 x^{3} + 2 x^{2} + 1$$ 
1 + x^5 + 2*x^2 + 2*x^3
Combinatorics [src] 
        /     4        3      2\
(1 + x)*\1 + x  - x - x  + 3*x /
$$\left(x + 1\right) \left(x^{4} - x^{3} + 3 x^{2} - x + 1\right)$$ 
(1 + x)*(1 + x^4 - x - x^3 + 3*x^2)
Numerical answer [src] 
1.0 + x^5 + 2.0*x^2 + 2.0*x^3
1.0 + x^5 + 2.0*x^2 + 2.0*x^3
Powers [src] 
     5      2      3
1 + x  + 2*x  + 2*x
$$x^{5} + 2 x^{3} + 2 x^{2} + 1$$ 
1 + x^5 + 2*x^2 + 2*x^3
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