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Simplificación de expresiones/ Descomposición de multiplicadores/ x^3+4*x^2+x-4

Factorizar el polinomio x^3+4*x^2+x-4

Expresión a simplificar:

Solución

Ha introducido [src] 
 3      2        
x  + 4*x  + x - 4
$$\left(x + \left(x^{3} + 4 x^{2}\right)\right) - 4$$ 
x^3 + 4*x^2 + x - 4
Factorización [src] 
/             ________________                                                          \ /             ________________                                                          \ /             ________________                          \
|            /          _____  /          ___\                                          | |            /          _____  /          ___\                                          | |            /          _____                           |
|    4      /  8    I*\/ 237   |  1   I*\/ 3 |                      13                  | |    4      /  8    I*\/ 237   |  1   I*\/ 3 |                      13                  | |    4      /  8    I*\/ 237                13          |
|x + - - 3 /   -- + --------- *|- - - -------| - ---------------------------------------|*|x + - - 3 /   -- + --------- *|- - + -------| - ---------------------------------------|*|x + - - 3 /   -- + ---------  - -----------------------|
|    3   \/    27       9      \  2      2   /                          ________________| |    3   \/    27       9      \  2      2   /                          ________________| |    3   \/    27       9               ________________|
|                                                  /          ___\     /          _____ | |                                                  /          ___\     /          _____ | |                                      /          _____ |
|                                                  |  1   I*\/ 3 |    /  8    I*\/ 237  | |                                                  |  1   I*\/ 3 |    /  8    I*\/ 237  | |                                     /  8    I*\/ 237  |
|                                                9*|- - - -------|*3 /   -- + --------- | |                                                9*|- - + -------|*3 /   -- + --------- | |                                9*3 /   -- + --------- |
\                                                  \  2      2   / \/    27       9     / \                                                  \  2      2   / \/    27       9     / \                                  \/    27       9     /
$$\left(x + \left(\frac{4}{3} - \frac{13}{9 \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{8}{27} + \frac{\sqrt{237} i}{9}}} - \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{8}{27} + \frac{\sqrt{237} i}{9}}\right)\right) \left(x + \left(\frac{4}{3} - \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{8}{27} + \frac{\sqrt{237} i}{9}} - \frac{13}{9 \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{8}{27} + \frac{\sqrt{237} i}{9}}}\right)\right) \left(x + \left(\frac{4}{3} - \sqrt[3]{\frac{8}{27} + \frac{\sqrt{237} i}{9}} - \frac{13}{9 \sqrt[3]{\frac{8}{27} + \frac{\sqrt{237} i}{9}}}\right)\right)$$ 
((x + 4/3 - (8/27 + i*sqrt(237)/9)^(1/3)*(-1/2 - i*sqrt(3)/2) - 13/(9*(-1/2 - i*sqrt(3)/2)*(8/27 + i*sqrt(237)/9)^(1/3)))*(x + 4/3 - (8/27 + i*sqrt(237)/9)^(1/3)*(-1/2 + i*sqrt(3)/2) - 13/(9*(-1/2 + i*sqrt(3)/2)*(8/27 + i*sqrt(237)/9)^(1/3))))*(x + 4/3 - (8/27 + i*sqrt(237)/9)^(1/3) - 13/(9*(8/27 + i*sqrt(237)/9)^(1/3)))
Simplificación general [src] 
          3      2
-4 + x + x  + 4*x
$$x^{3} + 4 x^{2} + x - 4$$ 
-4 + x + x^3 + 4*x^2
Respuesta numérica [src] 
-4.0 + x + x^3 + 4.0*x^2
-4.0 + x + x^3 + 4.0*x^2
Parte trigonométrica [src] 
          3      2
-4 + x + x  + 4*x
$$x^{3} + 4 x^{2} + x - 4$$ 
-4 + x + x^3 + 4*x^2
Denominador común [src] 
          3      2
-4 + x + x  + 4*x
$$x^{3} + 4 x^{2} + x - 4$$ 
-4 + x + x^3 + 4*x^2
Compilar la expresión [src] 
          3      2
-4 + x + x  + 4*x
$$x^{3} + 4 x^{2} + x - 4$$ 
-4 + x + x^3 + 4*x^2
Unión de expresiones racionales [src] 
-4 + x*(1 + x*(4 + x))
$$x \left(x \left(x + 4\right) + 1\right) - 4$$ 
-4 + x*(1 + x*(4 + x))
Combinatoria [src] 
          3      2
-4 + x + x  + 4*x
$$x^{3} + 4 x^{2} + x - 4$$ 
-4 + x + x^3 + 4*x^2
Potencias [src] 
          3      2
-4 + x + x  + 4*x
$$x^{3} + 4 x^{2} + x - 4$$ 
-4 + x + x^3 + 4*x^2
Denominador racional [src] 
          3      2
-4 + x + x  + 4*x
$$x^{3} + 4 x^{2} + x - 4$$ 
-4 + x + x^3 + 4*x^2
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