Mister Exam
Factor polynomial x^3/10-27*x^2/10+27*x/10+5
The solution
You have entered
[src]
3 2 x 27*x 27*x -- - ----- + ---- + 5 10 10 10
$$\left(\frac{27 x}{10} + \left(\frac{x^{3}}{10} - \frac{27 x^{2}}{10}\right)\right) + 5$$
x^3/10 - 27*x^2/10 + (27*x)/10 + 5
Fraction decomposition
[src]
5 - 27*x^2/10 + x^3/10 + 27*x/10
$$\frac{x^{3}}{10} - \frac{27 x^{2}}{10} + \frac{27 x}{10} + 5$$
2 3
27*x x 27*x
5 - ----- + -- + ----
10 10 10
Factorization
[src]
/ _____________________ \ / _____________________ \ / _____________________ \ | / ________ / ___\ | | / ________ / ___\ | | / ________ | | / 1165 I*\/ 135767 | 1 I*\/ 3 | 72 | | / 1165 I*\/ 135767 | 1 I*\/ 3 | 72 | | / 1165 I*\/ 135767 72 | |x + -9 - 3 / ---- + ------------ *|- - - -------| - ------------------------------------------|*|x + -9 - 3 / ---- + ------------ *|- - + -------| - ------------------------------------------|*|x + -9 - 3 / ---- + ------------ - --------------------------| | \/ 2 2 \ 2 2 / _____________________| | \/ 2 2 \ 2 2 / _____________________| | \/ 2 2 _____________________| | / ___\ / ________ | | / ___\ / ________ | | / ________ | | | 1 I*\/ 3 | / 1165 I*\/ 135767 | | | 1 I*\/ 3 | / 1165 I*\/ 135767 | | / 1165 I*\/ 135767 | | |- - - -------|*3 / ---- + ------------ | | |- - + -------|*3 / ---- + ------------ | | 3 / ---- + ------------ | \ \ 2 2 / \/ 2 2 / \ \ 2 2 / \/ 2 2 / \ \/ 2 2 /
$$\left(x + \left(-9 - \frac{72}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1165}{2} + \frac{\sqrt{135767} i}{2}}} - \left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1165}{2} + \frac{\sqrt{135767} i}{2}}\right)\right) \left(x + \left(-9 - \left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1165}{2} + \frac{\sqrt{135767} i}{2}} - \frac{72}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{1165}{2} + \frac{\sqrt{135767} i}{2}}}\right)\right) \left(x + \left(-9 - \sqrt[3]{\frac{1165}{2} + \frac{\sqrt{135767} i}{2}} - \frac{72}{\sqrt[3]{\frac{1165}{2} + \frac{\sqrt{135767} i}{2}}}\right)\right)$$
((x - 9 - (1165/2 + i*sqrt(135767)/2)^(1/3)*(-1/2 - i*sqrt(3)/2) - 72/((-1/2 - i*sqrt(3)/2)*(1165/2 + i*sqrt(135767)/2)^(1/3)))*(x - 9 - (1165/2 + i*sqrt(135767)/2)^(1/3)*(-1/2 + i*sqrt(3)/2) - 72/((-1/2 + i*sqrt(3)/2)*(1165/2 + i*sqrt(135767)/2)^(1/3))))*(x - 9 - (1165/2 + i*sqrt(135767)/2)^(1/3) - 72/(1165/2 + i*sqrt(135767)/2)^(1/3))
General simplification
[src]
2 3
27*x x 27*x
5 - ----- + -- + ----
10 10 10
$$\frac{x^{3}}{10} - \frac{27 x^{2}}{10} + \frac{27 x}{10} + 5$$
5 - 27*x^2/10 + x^3/10 + 27*x/10
Trigonometric part
[src]
2 3
27*x x 27*x
5 - ----- + -- + ----
10 10 10
$$\frac{x^{3}}{10} - \frac{27 x^{2}}{10} + \frac{27 x}{10} + 5$$
5 - 27*x^2/10 + x^3/10 + 27*x/10
Powers
[src]
2 3
27*x x 27*x
5 - ----- + -- + ----
10 10 10
$$\frac{x^{3}}{10} - \frac{27 x^{2}}{10} + \frac{27 x}{10} + 5$$
5 - 27*x^2/10 + x^3/10 + 27*x/10
Rational denominator
[src]
3 2
50 + x - 27*x + 27*x
----------------------
10
$$\frac{x^{3} - 27 x^{2} + 27 x + 50}{10}$$
(50 + x^3 - 27*x^2 + 27*x)/10
Combinatorics
[src]
2 3
27*x x 27*x
5 - ----- + -- + ----
10 10 10
$$\frac{x^{3}}{10} - \frac{27 x^{2}}{10} + \frac{27 x}{10} + 5$$
5 - 27*x^2/10 + x^3/10 + 27*x/10
Combining rational expressions
[src]
50 + x*(27 + x*(-27 + x))
-------------------------
10
$$\frac{x \left(x \left(x - 27\right) + 27\right) + 50}{10}$$
(50 + x*(27 + x*(-27 + x)))/10
Assemble expression
[src]
2 3
27*x x 27*x
5 - ----- + -- + ----
10 10 10
$$\frac{x^{3}}{10} - \frac{27 x^{2}}{10} + \frac{27 x}{10} + 5$$
5 - 27*x^2/10 + x^3/10 + 27*x/10
Common denominator
[src]
2 3
27*x x 27*x
5 - ----- + -- + ----
10 10 10
$$\frac{x^{3}}{10} - \frac{27 x^{2}}{10} + \frac{27 x}{10} + 5$$
5 - 27*x^2/10 + x^3/10 + 27*x/10