<s>[INST] By viewing the polynomials as a difference of two squares, factorise the following polynomials. By viewing the polynomials as a difference of two squares, factorise the following polynomial:
$$x^4+x^2+1.$$
I searched but couldn't find a way to solve this
Edit: By using Hans Lundmark hint, I get:
$$(x^2+1)^2-x^2$$ 
Is it fully factorized? 
 [/INST] We don't factorization:
$$\dfrac2{x^4+ax^2+1}=\dfrac{x^2+1}{x^4+ax^2+1}-\dfrac{x^2-1}{x^4+ax^2+1}=\dfrac{1+\dfrac1{x^2}}{x^2+a+\dfrac1{x^2}}+\dfrac{1-\dfrac1{x^2}}{x^2+a+\dfrac1{x^2}}$$
Now as $\displaystyle\int\left(1\pm\dfrac1{x^2}\right)dx=x\mp\dfrac1x,$
for the first integral, choose $x-\dfrac1x=u$ and $x+\dfrac1x=v$ for the second
Use $x^2+\dfrac1{x^2}=\left(x+\dfrac1x\right)^2-2=\left(x-\dfrac1x\right)^2+2$ 
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