How do you factor a Polynomial that has 2 variables?

we can factorize it through factor the common factor

for example there is a polynomial 3x^2+x+6y^2+2y

we can have a simple grouping first , put x in a group and y in another

(3x^2+x) (+6y^2+2y)

by extracting the common factor ,

we can see x(3x+1)+2y(3y+1)

as both x(3x+1) and 2y(3y+1) have the same factor(3y+1) still

we need to factorize it also and it will become (x+2y)(3y+1)

factorization is done!

there is another way also 

please see https://www.khanacademy.org/math/algebra/multiplying-factoring-expression/factoring-quadratics-in-two-vari/e/factoring_polynomials_with_two_variables for more about factorizing this kind of polynomial 

hope this can help you