Question

3 x y - 5 x + 6 y - 10

Answer 1

What is your question ?

Answer 2

 1.1       Split       3xy + 6y - 5x - 10 
             into two 2-term polynomials 
              + 6y + 3xy   and     - 5x - 10
             This partition did not result in a factorization. We'll try another one:

             3xy + 6y   and     - 5x - 10
             This partition looks good

 1.2       Pull out from each binomial separately
             3xy + 6y   =   3y • (x + 2)
              - 5x - 10   =    - 5 • (x + 2)

 1.3       Add up to arrive at the desired factorization
             (3y - 5) • (x + 2)