Question 150732
First term : {{{2x^2}}}
{{{2x(x+4)=2x^3+8x^2}}}
{{{(2x^3-19x^2+x-15)-(2x^3+8x^2)=highlight(-27x^2+x-15)}}}
Second term : {{{-27x}}}
{{{-27x(x+4)=-27x^2-108x}}}
{{{highlight((-27x^2+x-15))-(-27x^2-108x)=highlight(109x-15)}}}
Third term: {{{109}}}
{{{109(x+4)=109x+436}}}
{{{highlight((109x-15))-(109x+436)=-451}}}Remainder term
Put it all together,
{{{(2x^3-19x^2+x-15)/(x+4)=2x^2-27x+109-451/(x+4)}}}