Remember to include the #0# value coefficients for #x^3# and the constant.
synthetic division
#{:
(,,color(brown)(x^4),color(brown)(x^3),color(brown)(x^2),color(brown)(x^1),color(brown)(x^0)),
(,"|",1,0,-2,+17,0),
(,"|",,2,4,4,84),
("----",,"----","----","----","----","----"),
(xx(color(cyan)(+2)),"|",color(blue)(1),color(blue)(2),color(blue)(2),color(blue)(21),color(red)(84)),
(,,color(brown)(x^3),color(brown)(x^2),color(brown)(x^1),color(brown)(x^0),color(brown)("Rem"))
:}#
...also remember that for synthetic division (by a monic binomial) the #color(cyan)("multiplier")# is the negative of the constant from the divisor.
polynomial long division
#{:
(,,x^3,+2x^2,+2x,21,),
(,,"----","----","----","----","----"),
(x-2,")",x^4,,-2x^2,+17x,),
(,,x^4,-2x^3,,,),
(,,"----","----",,,),
(,,,2x^3,-2x^2,,),
(,,,2x^3,-4x^2,,),
(,,,"----","------",,),
(,,,,2x^2,+17x,),
(,,,,2x^2,-4x,),
(,,,,"----","------",),
(,,,,,21x,),
(,,,,,21x,-84),
(,,,,,"----","-----"),
(,,,,,,84)
:}#
