Question 145483
{{{(6z^3 + 23z^2 + 27z) / (2z + 3)}}}
The 1st term of the answer is {{{3z^2}}} since
{{{3z^2*(2z + 3) = 6z^3 + 9z^2}}}
{{{6z^3 + 23z^2}}}
{{{-6z^3 - 9z^2}}}
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{{{14z^2}}}
The 2nd term of the answer is {{{7z}}} since
{{{7z*(2z + 3) = 14z^2 + 21z}}}
{{{14z^2 + 27z}}}
{{{-14z^2 - 21z}}}
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{{{6z}}} (remainder)
So, the complete answer is
{{{3z^2 + 7z + (6z/(2z + 3))}}}
You can check this by multiplying it by {{{2z + 3}}}