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Expression simplification/ Factorization polynomials/ x^8-15*x^4-16

Factor polynomial x^8-15*x^4-16

An expression to simplify:

The solution

You have entered [src] 
 8       4     
x  - 15*x  - 16
$$\left(x^{8} - 15 x^{4}\right) - 16$$ 
x^8 - 15*x^4 - 16
General simplification [src] 
       8       4
-16 + x  - 15*x
$$x^{8} - 15 x^{4} - 16$$ 
-16 + x^8 - 15*x^4
Factorization [src] 
                                    /      ___       ___\ /      ___       ___\ /        ___       ___\ /        ___       ___\
                                    |    \/ 2    I*\/ 2 | |    \/ 2    I*\/ 2 | |      \/ 2    I*\/ 2 | |      \/ 2    I*\/ 2 |
(x + 2)*(x - 2)*(x + 2*I)*(x - 2*I)*|x + ----- + -------|*|x + ----- - -------|*|x + - ----- + -------|*|x + - ----- - -------|
                                    \      2        2   / \      2        2   / \        2        2   / \        2        2   /
$$\left(x - 2\right) \left(x + 2\right) \left(x + 2 i\right) \left(x - 2 i\right) \left(x + \left(\frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}\right)\right) \left(x + \left(\frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}\right)\right) \left(x + \left(- \frac{\sqrt{2}}{2} + \frac{\sqrt{2} i}{2}\right)\right) \left(x + \left(- \frac{\sqrt{2}}{2} - \frac{\sqrt{2} i}{2}\right)\right)$$ 
(((((((x + 2)*(x - 2))*(x + 2*i))*(x - 2*i))*(x + sqrt(2)/2 + i*sqrt(2)/2))*(x + sqrt(2)/2 - i*sqrt(2)/2))*(x - sqrt(2)/2 + i*sqrt(2)/2))*(x - sqrt(2)/2 - i*sqrt(2)/2)
Rational denominator [src] 
       8       4
-16 + x  - 15*x
$$x^{8} - 15 x^{4} - 16$$ 
-16 + x^8 - 15*x^4
Powers [src] 
       8       4
-16 + x  - 15*x
$$x^{8} - 15 x^{4} - 16$$ 
-16 + x^8 - 15*x^4
Trigonometric part [src] 
       8       4
-16 + x  - 15*x
$$x^{8} - 15 x^{4} - 16$$ 
-16 + x^8 - 15*x^4
Common denominator [src] 
       8       4
-16 + x  - 15*x
$$x^{8} - 15 x^{4} - 16$$ 
-16 + x^8 - 15*x^4
Assemble expression [src] 
       8       4
-16 + x  - 15*x
$$x^{8} - 15 x^{4} - 16$$ 
-16 + x^8 - 15*x^4
Numerical answer [src] 
-16.0 + x^8 - 15.0*x^4
-16.0 + x^8 - 15.0*x^4
Combinatorics [src] 
/     4\                  /     2\
\1 + x /*(-2 + x)*(2 + x)*\4 + x /
$$\left(x - 2\right) \left(x + 2\right) \left(x^{2} + 4\right) \left(x^{4} + 1\right)$$ 
(1 + x^4)*(-2 + x)*(2 + x)*(4 + x^2)
Combining rational expressions [src] 
       4 /       4\
-16 + x *\-15 + x /
$$x^{4} \left(x^{4} - 15\right) - 16$$ 
-16 + x^4*(-15 + x^4)
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