Set up as if doing a standard long division
#{:
(,,"-----","-----","-----"),
(n+2,")",n^2,-11n,-26)
:}#
The leading term of the divisor #color(green)(n)# divides into the leading term of the dividend #color(blue)(n^2)#, #color(red)(n)# times
#{:
(,,color(red)(n),,),
(,,"-----","-----","-----"),
(color(green)(n)+2,")",color(blue)(n^2),-11n,-26)
:}#
Multiply the divisor #color(green)(n+2)# by the term just written in the quotient (#color(red)(n)#) giving a product of #color(cyan)(n^2+2n)#
and subtract this product from the dividend giving a difference of #color(blue)(-13n)# and "bring down the next term, #color(orange)(-26)#
#{:
(,,color(red)(n),,),
(,,"-----","-----","-----"),
(color(green)(n+2),")",n^2,-11n,-26),
(,,color(cyan)(n^2),color(cyan)(+2n),),
(,,"-----","-----",),
(,,,color(blue)(-13n),color(orange)(-26))
:}#
Repeat this process to get:
#{:
(,,n,-13,),
(,,"-----","-----","-----"),
(n+2,")",n^2,-11n,-26),
(,,n^2,+2n,),
(,,"-----","-----",),
(,,,-13n,-26),
(,,,-13n,-26),
(,,,"-----","-----"),
(,,,,0)
:}#
