Is there some database or software to look for patterns in polynomials?

Question

Like if I am looking at these polynomials,

$$x^8-8x^6+20x^4-16x^2+3$$

$$x^{10}-12x^8+48x^6-72x^4+33x^2$$

$$x^{12}-16x^{10}+88x^8-192x^6+138x^4$$

And I want to know if they are members of some known sequence or not..

How can I go about it?

Answer 1

Have you ever played around with Wolfram Alpha?

Lots of super useful math tools. Try putting x^8−8x^6+20x^4−16x^2+3 vs x^10−12x^8+48x^6−72x^4+33x^2 in the prompt, for example.