It's pretty easy to factorise in stuff like this by just putting (2x )(x ) on your page and the answer comes apparent to you quite quickly, but I guess splitting the middle term becomes useful when you have a coefficient of x^2 with a lot of factors (not just 2 and 1)
Where is the "last" video that proves that method? I tried to prove it (for this example)and came up with: A*B = 20 and 2B + A = 13. B=20/A. 2(20/A) + A = 13. (40 + A^2)/A = 13 or 40 + A^2 = 13A or A^2 -13A + 40 = 0 and hence why your "13x = Ax +Bx, A*B = 2*20" Method works.