Answer:
see below
Step-by-step explanation:
If suffices to look at the last term. It must simplify to 4/(3w²), so the exponents of z must match in numerator and denominator, and the ratio of constants must reduce to 4/3.
The exponents of z have the right values in choices B and D, but the ratio of constants only matches in choice D. Looking at the rest of choice D, we see that we can factor 6w²z² from both numerator and denominator, then factor 2 from the remaining numerator to make it match the desired form.

Yes, there is an expanded algorithm for synthetic division involving nonlinear and non-monic divisors (check out the w.i.k.i.pedia page on "synthetic division", under the "Expanded sythetic division" section).
I estimated to 45 then divided 21 and got about 2.1
Answer: Quest 1 final result. (I looked all this up)
(2x -1) * (5x squared - 2x + 6)
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4
I could not find the work for part two but I got the answer: x=3,7