Question 149665
OK, bear with me because the software's a little cumbersome to show synthetic division.
Hopefully it's clear and straightforward.
First I'll show the multiplication of the term with the divisor.
Then the subtraction of the equation and the multiplication term. 
Then carry that sum down to the next multiplication. 
Let's start with {{{x^4}}} as the first term of the quotient, 
{{{x^4(x+2)=x^5+2x^4}}} 
{{{highlight(x^5+32)-(x^5+2x^4)=highlight( -2x^4+32)}}} 
Next term is {{{-2x^3}}},
{{{-2x^3(x+2)=-2x^4-4x^3}}}
{{{highlight(-2x^4+32)-(-2x^4-4x^3)=highlight(4x^3+32)}}}
Next term is {{{4x^2}}},
{{{4x^2(x+2)=4x^3+8x^2}}}
{{{highlight(4x^3+32)-(4x^3+8x^2)=highlight(-8x^2+32)}}}
Next term is {{{-8x}}},
{{{-8x(x+2)=-8x^2-16x}}}
{{{highlight(-8x^2+32)-(-8x^2-16x)=highlight(16x+32)}}}
Final term of the quotient is {{{16}}},
{{{16(x+2)=16x+32}}}
{{{highlight(16x+32)-(16x+32)=0}}}
The remainder is 0.
The quotient is 
{{{x^4-2x^3+4x^2-8x+16}}}
{{{(x^5+32)/(x+2)=x^4-2x^3+4x^2-8x+16}}}