Use synthetic division, divide the following and write down the quotient and remainder.
$$(6x^4+7x^3y-3x^2y^2+4xy^3+4y^4) \div (2x+3y)$$ How to start?

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accessdenied · Answer

So, I noticed that there are two variables involved here, and they make sort of that 'binomial expansion' pattern (x^4 y^0, x^3 y^1, x^2 y^2, etc.).

I am thinking that, to divide with this second variable and non-1 coefficient, we just pretend y is another coefficient/constant and divide as normal...
  The # we use for the division is the x-value for:   2x + 3y = 0
  Then I think we just set it up like this:
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