Question 165195
{{{(2x^3 + 3x^2 - 3x + 4) / (x+2)}}}
1st term = {{{2x^2}}}
{{{(x+2)*2x^2 = 2x^3 + 4x^2}}}
{{{3x^2 - 4x^2 =  -(x^2)}}}
2nd term = {{{-x}}}
{{{(x+2)*(-x) = -(x^2) - 2x}}}
{{{-3x + 2x = -x}}}
3rd term = {{{-1}}}
{{{(x+2)*(-1) = -x - 2}}}
{{{-x + 4 - (-x - 2) = 6}}}
The answer is
{{{2x^2 - x - 1 + 6/(x+2)}}} (last term is remainder)
check answer:
{{{(x+2)*(2x^2 - x - 1 + 6/(x+2))}}}
{{{2x^3 - x^2 - x + 6 + 4x^2 - 2x - 2 }}}
{{{2x^3 + 3x^2 - 3x + 4}}}
OK