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Factor polynomial:
x^3-3*x^2*y-4*x*y+12*y
x^3-3*x^3-x+3
x^3-3*x+3
x^3-5*x+1
Least common denominator:
z/(x-z)+(x+z)/z
n^2/n-4-8*n-16/n-4
(m+n/m-n-m-n/m+n)/(m-n/m+n+m+n/m-n)
(m^2+3*m/m^2+3*m+2-m^2-2*m/m^2-2*m-3)/1/m^2-m-6-5/m+1
Factor squared:
q^2+q+4
t^2+5*t*x+x^2
-q^2-2*q+3
t^2+4*t*x+3*x^2
How do you in partial fractions?:
(4x-1)/(x^2-4x+8)
(x+1)/(x^3-1)
(a^4-10*a^2+169)/(a^2+6*a+13)
x^2/(x-2)^2
Identical expressions
x^ three - five *x+ one
x cubed minus 5 multiply by x plus 1
x to the power of three minus five multiply by x plus one
x3-5*x+1
x³-5*x+1
x to the power of 3-5*x+1
x^3-5x+1
x3-5x+1
Similar expressions
x^3-5*x-1
x^3+5*x+1

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

Factor polynomial x^3-5*x+1

The solution

You have entered [src]

 3          
x  - 5*x + 1

$$\left(x^{3} - 5 x\right) + 1$$

x^3 - 5*x + 1

General simplification [src]

     3      
1 + x  - 5*x

$$x^{3} - 5 x + 1$$

1 + x^3 - 5*x

Factorization [src]

/                                                    ___________________                \ /                                                    ___________________                \ /                                    ___________________\
|                                                   /            ______  /          ___\| |                                                   /            ______  /          ___\| |                                   /            ______ |
|                                                  /  27   3*I*\/ 1419   |  1   I*\/ 3 || |                                                  /  27   3*I*\/ 1419   |  1   I*\/ 3 || |                                  /  27   3*I*\/ 1419  |
|                                               3 /   -- + ------------ *|- - - -------|| |                                               3 /   -- + ------------ *|- - + -------|| |                               3 /   -- + ------------ |
|                       5                       \/    2         2        \  2      2   /| |                       5                       \/    2         2        \  2      2   /| |               5               \/    2         2       |
|x + ---------------------------------------- + ----------------------------------------|*|x + ---------------------------------------- + ----------------------------------------|*|x + ------------------------ + ------------------------|
|                         ___________________                      3                    | |                         ___________________                      3                    | |         ___________________              3            |
|    /          ___\     /            ______                                            | |    /          ___\     /            ______                                            | |        /            ______                            |
|    |  1   I*\/ 3 |    /  27   3*I*\/ 1419                                             | |    |  1   I*\/ 3 |    /  27   3*I*\/ 1419                                             | |       /  27   3*I*\/ 1419                             |
|    |- - - -------|*3 /   -- + ------------                                            | |    |- - + -------|*3 /   -- + ------------                                            | |    3 /   -- + ------------                            |
\    \  2      2   / \/    2         2                                                  / \    \  2      2   / \/    2         2                                                  / \    \/    2         2                                  /

$$\left(x + \left(\frac{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{3 \sqrt{1419} i}{2}}}{3} + \frac{5}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{3 \sqrt{1419} i}{2}}}\right)\right) \left(x + \left(\frac{5}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{3 \sqrt{1419} i}{2}}} + \frac{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{27}{2} + \frac{3 \sqrt{1419} i}{2}}}{3}\right)\right) \left(x + \left(\frac{5}{\sqrt[3]{\frac{27}{2} + \frac{3 \sqrt{1419} i}{2}}} + \frac{\sqrt[3]{\frac{27}{2} + \frac{3 \sqrt{1419} i}{2}}}{3}\right)\right)$$

((x + 5/((-1/2 - i*sqrt(3)/2)*(27/2 + 3*i*sqrt(1419)/2)^(1/3)) + (27/2 + 3*i*sqrt(1419)/2)^(1/3)*(-1/2 - i*sqrt(3)/2)/3)*(x + 5/((-1/2 + i*sqrt(3)/2)*(27/2 + 3*i*sqrt(1419)/2)^(1/3)) + (27/2 + 3*i*sqrt(1419)/2)^(1/3)*(-1/2 + i*sqrt(3)/2)/3))*(x + 5/(27/2 + 3*i*sqrt(1419)/2)^(1/3) + (27/2 + 3*i*sqrt(1419)/2)^(1/3)/3)

Assemble expression [src]

     3      
1 + x  - 5*x

$$x^{3} - 5 x + 1$$

1 + x^3 - 5*x

Rational denominator [src]

     3      
1 + x  - 5*x

$$x^{3} - 5 x + 1$$

1 + x^3 - 5*x

Common denominator [src]

     3      
1 + x  - 5*x

$$x^{3} - 5 x + 1$$

1 + x^3 - 5*x

Numerical answer [src]

1.0 + x^3 - 5.0*x

1.0 + x^3 - 5.0*x

Combining rational expressions [src]

      /      2\
1 + x*\-5 + x /

$$x \left(x^{2} - 5\right) + 1$$

1 + x*(-5 + x^2)

Powers [src]

     3      
1 + x  - 5*x

$$x^{3} - 5 x + 1$$

1 + x^3 - 5*x

Trigonometric part [src]

     3      
1 + x  - 5*x

$$x^{3} - 5 x + 1$$

1 + x^3 - 5*x

Combinatorics [src]

     3      
1 + x  - 5*x

$$x^{3} - 5 x + 1$$

1 + x^3 - 5*x

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How to use it?

Identical expressions

Similar expressions

Factor polynomial x^3-5*x+1

The solution