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Simplificación de expresiones/ Descomposición de multiplicadores/ x^4+7*x^3+10*x^2-7*x+1

Factorizar el polinomio x^4+7*x^3+10*x^2-7*x+1

Expresión a simplificar:

Solución

Ha introducido [src] 
 4      3       2          
x  + 7*x  + 10*x  - 7*x + 1
(−7x+(10x2+(x4+7x3)))+1\left(- 7 x + \left(10 x^{2} + \left(x^{4} + 7 x^{3}\right)\right)\right) + 1 
x^4 + 7*x^3 + 10*x^2 - 7*x + 1
Factorización [src] 
                /          ____\ /          ____\                
/          ___\ |    3   \/ 13 | |    3   \/ 13 | /          ___\
\x + 2 - \/ 5 /*|x + - - ------|*|x + - + ------|*\x + 2 + \/ 5 /
                \    2     2   / \    2     2   /
(x+(32−132))(x+(2−5))(x+(32+132))(x+(2+5))\left(x + \left(\frac{3}{2} - \frac{\sqrt{13}}{2}\right)\right) \left(x + \left(2 - \sqrt{5}\right)\right) \left(x + \left(\frac{3}{2} + \frac{\sqrt{13}}{2}\right)\right) \left(x + \left(2 + \sqrt{5}\right)\right) 
(((x + 2 - sqrt(5))*(x + 3/2 - sqrt(13)/2))*(x + 3/2 + sqrt(13)/2))*(x + 2 + sqrt(5))
Simplificación general [src] 
     4            3       2
1 + x  - 7*x + 7*x  + 10*x
x4+7x3+10x2−7x+1x^{4} + 7 x^{3} + 10 x^{2} - 7 x + 1 
1 + x^4 - 7*x + 7*x^3 + 10*x^2
Denominador común [src] 
     4            3       2
1 + x  - 7*x + 7*x  + 10*x
x4+7x3+10x2−7x+1x^{4} + 7 x^{3} + 10 x^{2} - 7 x + 1 
1 + x^4 - 7*x + 7*x^3 + 10*x^2
Denominador racional [src] 
     4            3       2
1 + x  - 7*x + 7*x  + 10*x
x4+7x3+10x2−7x+1x^{4} + 7 x^{3} + 10 x^{2} - 7 x + 1 
1 + x^4 - 7*x + 7*x^3 + 10*x^2
Respuesta numérica [src] 
1.0 + x^4 + 10.0*x^2 + 7.0*x^3 - 7.0*x
1.0 + x^4 + 10.0*x^2 + 7.0*x^3 - 7.0*x
Parte trigonométrica [src] 
     4            3       2
1 + x  - 7*x + 7*x  + 10*x
x4+7x3+10x2−7x+1x^{4} + 7 x^{3} + 10 x^{2} - 7 x + 1 
1 + x^4 - 7*x + 7*x^3 + 10*x^2
Unión de expresiones racionales [src] 
1 + x*(-7 + x*(10 + x*(7 + x)))
x(x(x(x+7)+10)−7)+1x \left(x \left(x \left(x + 7\right) + 10\right) - 7\right) + 1 
1 + x*(-7 + x*(10 + x*(7 + x)))
Potencias [src] 
     4            3       2
1 + x  - 7*x + 7*x  + 10*x
x4+7x3+10x2−7x+1x^{4} + 7 x^{3} + 10 x^{2} - 7 x + 1 
1 + x^4 - 7*x + 7*x^3 + 10*x^2
Compilar la expresión [src] 
     4            3       2
1 + x  - 7*x + 7*x  + 10*x
x4+7x3+10x2−7x+1x^{4} + 7 x^{3} + 10 x^{2} - 7 x + 1 
1 + x^4 - 7*x + 7*x^3 + 10*x^2
Combinatoria [src] 
/      2      \ /      2      \
\-1 + x  + 3*x/*\-1 + x  + 4*x/
(x2+3x−1)(x2+4x−1)\left(x^{2} + 3 x - 1\right) \left(x^{2} + 4 x - 1\right) 
(-1 + x^2 + 3*x)*(-1 + x^2 + 4*x)
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