Mister Exam

Other calculators

Expression simplification/ Factorization polynomials/ x^8+x^6-92*x^4+9*x^2+81

Factor polynomial x^8+x^6-92*x^4+9*x^2+81

An expression to simplify:

The solution

You have entered [src] 
 8    6       4      2     
x  + x  - 92*x  + 9*x  + 81
$$\left(9 x^{2} + \left(- 92 x^{4} + \left(x^{8} + x^{6}\right)\right)\right) + 81$$ 
x^8 + x^6 - 92*x^4 + 9*x^2 + 81
General simplification [src] 
      6    8       4      2
81 + x  + x  - 92*x  + 9*x
$$x^{8} + x^{6} - 92 x^{4} + 9 x^{2} + 81$$ 
81 + x^6 + x^8 - 92*x^4 + 9*x^2
Factorization [src] 
                                /         _______________\ /         _______________\ /         _______________\ /         _______________\
                                |        /          ____ | |        /          ____ | |        /          ____ | |        /          ____ |
                                |       /    11   \/ 85  | |       /    11   \/ 85  | |       /    11   \/ 85  | |       /    11   \/ 85  |
(x + 3)*(x + 1)*(x - 1)*(x - 3)*|x +   /   - -- - ------ |*|x -   /   - -- - ------ |*|x +   /   - -- + ------ |*|x -   /   - -- + ------ |
                                \    \/      2      2    / \    \/      2      2    / \    \/      2      2    / \    \/      2      2    /
$$\left(x + 1\right) \left(x + 3\right) \left(x - 1\right) \left(x - 3\right) \left(x + \sqrt{- \frac{11}{2} - \frac{\sqrt{85}}{2}}\right) \left(x - \sqrt{- \frac{11}{2} - \frac{\sqrt{85}}{2}}\right) \left(x + \sqrt{- \frac{11}{2} + \frac{\sqrt{85}}{2}}\right) \left(x - \sqrt{- \frac{11}{2} + \frac{\sqrt{85}}{2}}\right)$$ 
(((((((x + 3)*(x + 1))*(x - 1))*(x - 3))*(x + sqrt(-11/2 - sqrt(85)/2)))*(x - sqrt(-11/2 - sqrt(85)/2)))*(x + sqrt(-11/2 + sqrt(85)/2)))*(x - sqrt(-11/2 + sqrt(85)/2))
Rational denominator [src] 
      6    8       4      2
81 + x  + x  - 92*x  + 9*x
$$x^{8} + x^{6} - 92 x^{4} + 9 x^{2} + 81$$ 
81 + x^6 + x^8 - 92*x^4 + 9*x^2
Numerical answer [src] 
81.0 + x^6 + x^8 + 9.0*x^2 - 92.0*x^4
81.0 + x^6 + x^8 + 9.0*x^2 - 92.0*x^4
Assemble expression [src] 
      6    8       4      2
81 + x  + x  - 92*x  + 9*x
$$x^{8} + x^{6} - 92 x^{4} + 9 x^{2} + 81$$ 
81 + x^6 + x^8 - 92*x^4 + 9*x^2
Combining rational expressions [src] 
      2 /     2 /       2 /     2\\\
81 + x *\9 + x *\-92 + x *\1 + x ///
$$x^{2} \left(x^{2} \left(x^{2} \left(x^{2} + 1\right) - 92\right) + 9\right) + 81$$ 
81 + x^2*(9 + x^2*(-92 + x^2*(1 + x^2)))
Common denominator [src] 
      6    8       4      2
81 + x  + x  - 92*x  + 9*x
$$x^{8} + x^{6} - 92 x^{4} + 9 x^{2} + 81$$ 
81 + x^6 + x^8 - 92*x^4 + 9*x^2
Trigonometric part [src] 
      6    8       4      2
81 + x  + x  - 92*x  + 9*x
$$x^{8} + x^{6} - 92 x^{4} + 9 x^{2} + 81$$ 
81 + x^6 + x^8 - 92*x^4 + 9*x^2
Combinatorics [src] 
                                  /     4       2\
(1 + x)*(-1 + x)*(-3 + x)*(3 + x)*\9 + x  + 11*x /
$$\left(x - 3\right) \left(x - 1\right) \left(x + 1\right) \left(x + 3\right) \left(x^{4} + 11 x^{2} + 9\right)$$ 
(1 + x)*(-1 + x)*(-3 + x)*(3 + x)*(9 + x^4 + 11*x^2)
Powers [src] 
      6    8       4      2
81 + x  + x  - 92*x  + 9*x
$$x^{8} + x^{6} - 92 x^{4} + 9 x^{2} + 81$$ 
81 + x^6 + x^8 - 92*x^4 + 9*x^2
    © Mister Exam – Calculator