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\polylongdiv{x^3+1}{x+2} using polynom package gives the following!

\polylongdiv{x^3+1}{x+2}

  1. The first mark : I'd like to remove the space between the parenthesis and the overline as marked.
  2. Next two marks : I'd like to write x³+2x² instead of -x³-2x². That is, I'd like to put the product of the divisor and the quotient without multiplying by a negative sign.
  3. If possible, I'd like to have faint zero co-efficient terms as shown below.

I'd like to get the result as follows. A parenthesis can be used instead of the vertical stroke between the divisor and the dividend.

What I want

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