Sr Examen
Factorizar el polinomio -x+t^24*x^2/2
Solución
Simplificación general
[src]
/ 24\
x*\-2 + x*t /
--------------
2
$$\frac{x \left(t^{24} x - 2\right)}{2}$$
x*(-2 + x*t^24)/2
Factorización
[src]
/ 13 13 \ / 13 13 \ / 13 13 \ / 13 13 \ / 13 13 13 13 \ / 13 13 13 13 \ / 13 13 13 13 \ / 13 13 13 13 \ / 13 13 13 13 \ / 13 13 13 13 \ / 13 13 13 13 \ / 13 13 13 13 \
/ ___ ___\ / ___ ___\ / ___ ___\ / ___ ___\ | -- ___ -- ___| | -- ___ -- ___| | -- ___ -- ___| | -- ___ -- ___| / ___ ___\ / ___ ___\ / ___ ___\ / ___ ___\ | -- ___ -- ___ -- ___ -- ___| | -- ___ -- ___ -- ___ -- ___| | -- ___ -- ___ -- ___ -- ___| | -- ___ -- ___ -- ___ -- ___| | -- ___ -- ___ -- ___ -- ___| | -- ___ -- ___ -- ___ -- ___| | -- ___ -- ___ -- ___ -- ___| | -- ___ -- ___ -- ___ -- ___|
| 24___ / 1 24___ ___ / 1 | | 24___ / 1 24___ ___ / 1 | | 24___ / 1 24___ ___ / 1 | | 24___ / 1 24___ ___ / 1 | | 24 / 1 24 / 1 | | 24 / 1 24 / 1 | | 24 / 1 24 / 1 | | 24 / 1 24 / 1 | | 24___ / 1 24___ ___ / 1 | | 24___ / 1 24___ ___ / 1 | | 24___ ___ / 1 24___ / 1 | | 24___ / 1 24___ ___ / 1 | | 24 / 1 24 / 1 24 ___ / 1 24 ___ / 1 | | 24 / 1 24 / 1 24 ___ / 1 24 ___ / 1 | | 24 / 1 24 / 1 24 ___ / 1 24 ___ / 1 | | 24 / 1 24 / 1 24 ___ / 1 24 ___ / 1 | | 24 / 1 24 / 1 24 ___ / 1 24 ___ / 1 | | 24 / 1 24 ___ / 1 24 / 1 24 ___ / 1 | | 24 / 1 24 ___ / 1 24 / 1 24 ___ / 1 | | 24 / 1 24 / 1 24 ___ / 1 24 ___ / 1 |
/ ___\ / ___\ / ___\ / ___\ | \/ 2 *24/ - I*\/ 2 *\/ 3 *24/ - | | \/ 2 *24/ - I*\/ 2 *\/ 3 *24/ - | | \/ 2 *24/ - I*\/ 2 *\/ 3 *24/ - | | \/ 2 *24/ - I*\/ 2 *\/ 3 *24/ - | | 2 *24/ - I*2 *24/ - | | 2 *24/ - I*2 *24/ - | | 2 *24/ - I*2 *24/ - | | 2 *24/ - I*2 *24/ - | | I*\/ 2 *24/ - \/ 2 *\/ 3 *24/ - | | I*\/ 2 *24/ - \/ 2 *\/ 3 *24/ - | | \/ 2 *\/ 3 *24/ - I*\/ 2 *24/ - | | I*\/ 2 *24/ - \/ 2 *\/ 3 *24/ - | | 2 *24/ - I*2 *24/ - 2 *\/ 3 *24/ - I*2 *\/ 3 *24/ - | | 2 *24/ - I*2 *24/ - 2 *\/ 3 *24/ - I*2 *\/ 3 *24/ - | | 2 *24/ - I*2 *24/ - 2 *\/ 3 *24/ - I*2 *\/ 3 *24/ - | | 2 *24/ - I*2 *24/ - 2 *\/ 3 *24/ - I*2 *\/ 3 *24/ - | | 2 *24/ - I*2 *24/ - 2 *\/ 3 *24/ - I*2 *\/ 3 *24/ - | | 2 *24/ - 2 *\/ 3 *24/ - I*2 *24/ - I*2 *\/ 3 *24/ - | | 2 *24/ - 2 *\/ 3 *24/ - I*2 *24/ - I*2 *\/ 3 *24/ - | | 2 *24/ - I*2 *24/ - 2 *\/ 3 *24/ - I*2 *\/ 3 *24/ - |
| 24___ / 1 | | 24___ / 1 | | 24___ / 1 | | 24___ / 1 | | \/ x \/ x | | \/ x \/ x | | \/ x \/ x | | \/ x \/ x | | \/ x \/ x | | \/ x \/ x | | \/ x \/ x | | \/ x \/ x | | \/ x \/ x | | \/ x \/ x | | \/ x \/ x | | \/ x \/ x | | \/ x \/ x \/ x \/ x | | \/ x \/ x \/ x \/ x | | \/ x \/ x \/ x \/ x | | \/ x \/ x \/ x \/ x | | \/ x \/ x \/ x \/ x | | \/ x \/ x \/ x \/ x | | \/ x \/ x \/ x \/ x | | \/ x \/ x \/ x \/ x |
|t + \/ 2 *24/ - |*|t - \/ 2 *24/ - |*|t + I*\/ 2 *24/ - |*|t - I*\/ 2 *24/ - |*|t + ------------- + ---------------------|*|t + ------------- - ---------------------|*|t + - ------------- + ---------------------|*|t + - ------------- - ---------------------|*|t + ----------- + -------------|*|t + ----------- - -------------|*|t + - ----------- + -------------|*|t + - ----------- - -------------|*|t + --------------- + -------------------|*|t + - --------------- + -------------------|*|t + - ------------------- + ---------------|*|t + - --------------- - -------------------|*|t + ----------- - ------------- - ----------------- - -------------------|*|t + ----------- + ------------- - ----------------- + -------------------|*|t + - ----------- + ------------- - ----------------- - -------------------|*|t + - ----------- - ------------- - ----------------- + -------------------|*|t + ----------- + ------------- + ----------------- - -------------------|*|t + ----------- + ----------------- - ------------- + -------------------|*|t + - ----------- + ----------------- - ------------- - -------------------|*|t + - ----------- + ------------- + ----------------- + -------------------|*x
\ \/ x / \ \/ x / \ \/ x / \ \/ x / \ 2 2 / \ 2 2 / \ 2 2 / \ 2 2 / \ 2 2 / \ 2 2 / \ 2 2 / \ 2 2 / \ 2 2 / \ 2 2 / \ 2 2 / \ 2 2 / \ 4 4 4 4 / \ 4 4 4 4 / \ 4 4 4 4 / \ 4 4 4 4 / \ 4 4 4 4 / \ 4 4 4 4 / \ 4 4 4 4 / \ 4 4 4 4 /
$$x \left(t - \sqrt[24]{2} \sqrt[24]{\frac{1}{x}}\right) \left(t + \sqrt[24]{2} \sqrt[24]{\frac{1}{x}}\right) \left(t + \sqrt[24]{2} i \sqrt[24]{\frac{1}{x}}\right) \left(t - \sqrt[24]{2} i \sqrt[24]{\frac{1}{x}}\right) \left(t + \left(\frac{\sqrt[24]{2} \sqrt[24]{\frac{1}{x}}}{2} + \frac{\sqrt[24]{2} \sqrt{3} i \sqrt[24]{\frac{1}{x}}}{2}\right)\right) \left(t + \left(\frac{\sqrt[24]{2} \sqrt[24]{\frac{1}{x}}}{2} - \frac{\sqrt[24]{2} \sqrt{3} i \sqrt[24]{\frac{1}{x}}}{2}\right)\right) \left(t + \left(- \frac{\sqrt[24]{2} \sqrt[24]{\frac{1}{x}}}{2} + \frac{\sqrt[24]{2} \sqrt{3} i \sqrt[24]{\frac{1}{x}}}{2}\right)\right) \left(t + \left(- \frac{\sqrt[24]{2} \sqrt[24]{\frac{1}{x}}}{2} - \frac{\sqrt[24]{2} \sqrt{3} i \sqrt[24]{\frac{1}{x}}}{2}\right)\right) \left(t + \left(\frac{2^{\frac{13}{24}} \sqrt[24]{\frac{1}{x}}}{2} + \frac{2^{\frac{13}{24}} i \sqrt[24]{\frac{1}{x}}}{2}\right)\right) \left(t + \left(\frac{2^{\frac{13}{24}} \sqrt[24]{\frac{1}{x}}}{2} - \frac{2^{\frac{13}{24}} i \sqrt[24]{\frac{1}{x}}}{2}\right)\right) \left(t + \left(- \frac{2^{\frac{13}{24}} \sqrt[24]{\frac{1}{x}}}{2} + \frac{2^{\frac{13}{24}} i \sqrt[24]{\frac{1}{x}}}{2}\right)\right) \left(t + \left(- \frac{2^{\frac{13}{24}} \sqrt[24]{\frac{1}{x}}}{2} - \frac{2^{\frac{13}{24}} i \sqrt[24]{\frac{1}{x}}}{2}\right)\right) \left(t + \left(\frac{\sqrt[24]{2} \sqrt{3} \sqrt[24]{\frac{1}{x}}}{2} + \frac{\sqrt[24]{2} i \sqrt[24]{\frac{1}{x}}}{2}\right)\right) \left(t + \left(\frac{\sqrt[24]{2} \sqrt{3} \sqrt[24]{\frac{1}{x}}}{2} - \frac{\sqrt[24]{2} i \sqrt[24]{\frac{1}{x}}}{2}\right)\right) \left(t + \left(- \frac{\sqrt[24]{2} \sqrt{3} \sqrt[24]{\frac{1}{x}}}{2} + \frac{\sqrt[24]{2} i \sqrt[24]{\frac{1}{x}}}{2}\right)\right) \left(t + \left(- \frac{\sqrt[24]{2} \sqrt{3} \sqrt[24]{\frac{1}{x}}}{2} - \frac{\sqrt[24]{2} i \sqrt[24]{\frac{1}{x}}}{2}\right)\right) \left(t + \left(- \frac{2^{\frac{13}{24}} \sqrt{3} \sqrt[24]{\frac{1}{x}}}{4} + \frac{2^{\frac{13}{24}} \sqrt[24]{\frac{1}{x}}}{4} - \frac{2^{\frac{13}{24}} \sqrt{3} i \sqrt[24]{\frac{1}{x}}}{4} - \frac{2^{\frac{13}{24}} i \sqrt[24]{\frac{1}{x}}}{4}\right)\right) \left(t + \left(- \frac{2^{\frac{13}{24}} \sqrt{3} \sqrt[24]{\frac{1}{x}}}{4} + \frac{2^{\frac{13}{24}} \sqrt[24]{\frac{1}{x}}}{4} + \frac{2^{\frac{13}{24}} i \sqrt[24]{\frac{1}{x}}}{4} + \frac{2^{\frac{13}{24}} \sqrt{3} i \sqrt[24]{\frac{1}{x}}}{4}\right)\right) \left(t + \left(- \frac{2^{\frac{13}{24}} \sqrt{3} \sqrt[24]{\frac{1}{x}}}{4} - \frac{2^{\frac{13}{24}} \sqrt[24]{\frac{1}{x}}}{4} - \frac{2^{\frac{13}{24}} \sqrt{3} i \sqrt[24]{\frac{1}{x}}}{4} + \frac{2^{\frac{13}{24}} i \sqrt[24]{\frac{1}{x}}}{4}\right)\right) \left(t + \left(- \frac{2^{\frac{13}{24}} \sqrt{3} \sqrt[24]{\frac{1}{x}}}{4} - \frac{2^{\frac{13}{24}} \sqrt[24]{\frac{1}{x}}}{4} - \frac{2^{\frac{13}{24}} i \sqrt[24]{\frac{1}{x}}}{4} + \frac{2^{\frac{13}{24}} \sqrt{3} i \sqrt[24]{\frac{1}{x}}}{4}\right)\right) \left(t + \left(\frac{2^{\frac{13}{24}} \sqrt[24]{\frac{1}{x}}}{4} + \frac{2^{\frac{13}{24}} \sqrt{3} \sqrt[24]{\frac{1}{x}}}{4} - \frac{2^{\frac{13}{24}} \sqrt{3} i \sqrt[24]{\frac{1}{x}}}{4} + \frac{2^{\frac{13}{24}} i \sqrt[24]{\frac{1}{x}}}{4}\right)\right) \left(t + \left(\frac{2^{\frac{13}{24}} \sqrt[24]{\frac{1}{x}}}{4} + \frac{2^{\frac{13}{24}} \sqrt{3} \sqrt[24]{\frac{1}{x}}}{4} - \frac{2^{\frac{13}{24}} i \sqrt[24]{\frac{1}{x}}}{4} + \frac{2^{\frac{13}{24}} \sqrt{3} i \sqrt[24]{\frac{1}{x}}}{4}\right)\right) \left(t + \left(- \frac{2^{\frac{13}{24}} \sqrt[24]{\frac{1}{x}}}{4} + \frac{2^{\frac{13}{24}} \sqrt{3} \sqrt[24]{\frac{1}{x}}}{4} - \frac{2^{\frac{13}{24}} \sqrt{3} i \sqrt[24]{\frac{1}{x}}}{4} - \frac{2^{\frac{13}{24}} i \sqrt[24]{\frac{1}{x}}}{4}\right)\right) \left(t + \left(- \frac{2^{\frac{13}{24}} \sqrt[24]{\frac{1}{x}}}{4} + \frac{2^{\frac{13}{24}} \sqrt{3} \sqrt[24]{\frac{1}{x}}}{4} + \frac{2^{\frac{13}{24}} i \sqrt[24]{\frac{1}{x}}}{4} + \frac{2^{\frac{13}{24}} \sqrt{3} i \sqrt[24]{\frac{1}{x}}}{4}\right)\right)$$
((((((((((((((((((((((((t + 2^(1/24)*(1/x)^(1/24))*(t - 2^(1/24)*(1/x)^(1/24)))*(t + i*2^(1/24)*(1/x)^(1/24)))*(t - i*2^(1/24)*(1/x)^(1/24)))*(t + 2^(1/24)*(1/x)^(1/24)/2 + i*2^(1/24)*sqrt(3)*(1/x)^(1/24)/2))*(t + 2^(1/24)*(1/x)^(1/24)/2 - i*2^(1/24)*sqrt(3)*(1/x)^(1/24)/2))*(t - 2^(1/24)*(1/x)^(1/24)/2 + i*2^(1/24)*sqrt(3)*(1/x)^(1/24)/2))*(t - 2^(1/24)*(1/x)^(1/24)/2 - i*2^(1/24)*sqrt(3)*(1/x)^(1/24)/2))*(t + 2^(13/24)*(1/x)^(1/24)/2 + i*2^(13/24)*(1/x)^(1/24)/2))*(t + 2^(13/24)*(1/x)^(1/24)/2 - i*2^(13/24)*(1/x)^(1/24)/2))*(t - 2^(13/24)*(1/x)^(1/24)/2 + i*2^(13/24)*(1/x)^(1/24)/2))*(t - 2^(13/24)*(1/x)^(1/24)/2 - i*2^(13/24)*(1/x)^(1/24)/2))*(t + i*2^(1/24)*(1/x)^(1/24)/2 + 2^(1/24)*sqrt(3)*(1/x)^(1/24)/2))*(t - i*2^(1/24)*(1/x)^(1/24)/2 + 2^(1/24)*sqrt(3)*(1/x)^(1/24)/2))*(t - 2^(1/24)*sqrt(3)*(1/x)^(1/24)/2 + i*2^(1/24)*(1/x)^(1/24)/2))*(t - i*2^(1/24)*(1/x)^(1/24)/2 - 2^(1/24)*sqrt(3)*(1/x)^(1/24)/2))*(t + 2^(13/24)*(1/x)^(1/24)/4 - i*2^(13/24)*(1/x)^(1/24)/4 - 2^(13/24)*sqrt(3)*(1/x)^(1/24)/4 - i*2^(13/24)*sqrt(3)*(1/x)^(1/24)/4))*(t + 2^(13/24)*(1/x)^(1/24)/4 + i*2^(13/24)*(1/x)^(1/24)/4 - 2^(13/24)*sqrt(3)*(1/x)^(1/24)/4 + i*2^(13/24)*sqrt(3)*(1/x)^(1/24)/4))*(t - 2^(13/24)*(1/x)^(1/24)/4 + i*2^(13/24)*(1/x)^(1/24)/4 - 2^(13/24)*sqrt(3)*(1/x)^(1/24)/4 - i*2^(13/24)*sqrt(3)*(1/x)^(1/24)/4))*(t - 2^(13/24)*(1/x)^(1/24)/4 - i*2^(13/24)*(1/x)^(1/24)/4 - 2^(13/24)*sqrt(3)*(1/x)^(1/24)/4 + i*2^(13/24)*sqrt(3)*(1/x)^(1/24)/4))*(t + 2^(13/24)*(1/x)^(1/24)/4 + i*2^(13/24)*(1/x)^(1/24)/4 + 2^(13/24)*sqrt(3)*(1/x)^(1/24)/4 - i*2^(13/24)*sqrt(3)*(1/x)^(1/24)/4))*(t + 2^(13/24)*(1/x)^(1/24)/4 + 2^(13/24)*sqrt(3)*(1/x)^(1/24)/4 - i*2^(13/24)*(1/x)^(1/24)/4 + i*2^(13/24)*sqrt(3)*(1/x)^(1/24)/4))*(t - 2^(13/24)*(1/x)^(1/24)/4 + 2^(13/24)*sqrt(3)*(1/x)^(1/24)/4 - i*2^(13/24)*(1/x)^(1/24)/4 - i*2^(13/24)*sqrt(3)*(1/x)^(1/24)/4))*(t - 2^(13/24)*(1/x)^(1/24)/4 + i*2^(13/24)*(1/x)^(1/24)/4 + 2^(13/24)*sqrt(3)*(1/x)^(1/24)/4 + i*2^(13/24)*sqrt(3)*(1/x)^(1/24)/4))*x
Denominador racional
[src]
24 2
-2*x + t *x
-------------
2
$$\frac{t^{24} x^{2} - 2 x}{2}$$
(-2*x + t^24*x^2)/2
Unión de expresiones racionales
[src]
/ 24\
x*\-2 + x*t /
--------------
2
$$\frac{x \left(t^{24} x - 2\right)}{2}$$
x*(-2 + x*t^24)/2
Combinatoria
[src]
/ 24\
x*\-2 + x*t /
--------------
2
$$\frac{x \left(t^{24} x - 2\right)}{2}$$
x*(-2 + x*t^24)/2