Largest linear Independent subset of n polynomials

Question

There are n polynomials in below format:

x(i)  
x(i)+1  
x(i)+x(k)  
x(i)+x(k)+1  
...  

We want to extract largest possible linear independant subset of above polynomials
I have tried Gassian elimination but it's too slow.
Any help is appreciated

Answer 1

As I searched, the solution is to use SVD or QR Decomposition.
These are the case.
Regards