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Expression simplification/ Factorization polynomials/ x^4+x²-20

Factor polynomial x^4+x²-20

An expression to simplify:

The solution

You have entered [src] 
 4    2     
x  + x  - 20
$$\left(x^{4} + x^{2}\right) - 20$$ 
x^4 + x^2 - 20
Factorization [src] 
                /        ___\ /        ___\
(x + 2)*(x - 2)*\x + I*\/ 5 /*\x - I*\/ 5 /
$$\left(x - 2\right) \left(x + 2\right) \left(x + \sqrt{5} i\right) \left(x - \sqrt{5} i\right)$$ 
(((x + 2)*(x - 2))*(x + i*sqrt(5)))*(x - i*sqrt(5))
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(x^{4} + x^{2}\right) - 20$$
To do this, let's use the formula
$$a x^{4} + b x^{2} + c = a \left(m + x^{2}\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = 1$$
$$b = 1$$
$$c = -20$$
Then
$$m = \frac{1}{2}$$
$$n = - \frac{81}{4}$$
So,
$$\left(x^{2} + \frac{1}{2}\right)^{2} - \frac{81}{4}$$
General simplification [src] 
       2    4
-20 + x  + x
$$x^{4} + x^{2} - 20$$ 
-20 + x^2 + x^4
Rational denominator [src] 
       2    4
-20 + x  + x
$$x^{4} + x^{2} - 20$$ 
-20 + x^2 + x^4
Trigonometric part [src] 
       2    4
-20 + x  + x
$$x^{4} + x^{2} - 20$$ 
-20 + x^2 + x^4
Numerical answer [src] 
-20.0 + x^2 + x^4
-20.0 + x^2 + x^4
Assemble expression [src] 
       2    4
-20 + x  + x
$$x^{4} + x^{2} - 20$$ 
-20 + x^2 + x^4
Powers [src] 
       2    4
-20 + x  + x
$$x^{4} + x^{2} - 20$$ 
-20 + x^2 + x^4
Common denominator [src] 
       2    4
-20 + x  + x
$$x^{4} + x^{2} - 20$$ 
-20 + x^2 + x^4
Combining rational expressions [src] 
       2 /     2\
-20 + x *\1 + x /
$$x^{2} \left(x^{2} + 1\right) - 20$$ 
-20 + x^2*(1 + x^2)
Combinatorics [src] 
                 /     2\
(-2 + x)*(2 + x)*\5 + x /
$$\left(x - 2\right) \left(x + 2\right) \left(x^{2} + 5\right)$$ 
(-2 + x)*(2 + x)*(5 + x^2)
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