Yo, by far my favourite method for polynomials of small degree is something which I've forgotten the name of! Comparison of factors or something?
Anyway, we write a general quadratic and note (2x-1)(ax^2+bx+c), then we note that the only way to get an x^3 is by the 2x * ax^2, so 2ax^3 = 2x^3 implies a = 1, then we note that the only way to get a constant is -1*c, so -c = -8, c= 8, this leaves the trickier b, which is like, 2x*c - bx right? Soooo
x(16-b) = 11x, aha! b is 5, just as you suspected.
This idea can be extended to polynomials of n degree, make a general polynomial of n-1 degree, but with big n this can get messy.
Edit: Seriously, what is that called, it's killing me.