To divide x^3-729x3−729 or x^3+0x^2+0x-729x3+0x2+0x−729 by x+2x+2
One Write the coefficients of xx in the dividend inside an upside-down division symbol.
color(white)(1)|color(white)(X)1" "color(white)(X)0color(white)(XX)0" "" "-7291∣X1 X0XX0 −729
color(white)(1)|" "color(white)(X)1∣ X
" "stackrel("—————————————)
Two As x-9=0 gives x=9 put 9 at the left.
9color(white)(X)|1" "color(white)(X)0color(white)(XX)0" "" "-729
color(white)(xx)|" "color(white)(XX)
" "stackrel("—————————————)
Three Drop the first coefficient of the dividend below the division symbol.
9color(white)(X)|1" "color(white)(X)0color(white)(XX)0" "" "-729
color(white)(xx)|" "color(white)(X)
" "stackrel("—————————————)
color(white)(xx)|color(white)()color(red)1
Four Multiply the result by the constant, and put the product in the next column.
9color(white)(X)|1" "color(white)(X)0color(white)(XX)0" "" "-729
color(white)(xx)|" "color(white)(Xx)9
" "stackrel("—————————————)
color(white)(xx)|color(white)()color(blue)1
Five Add down the column.
9color(white)(X)|1" "color(white)(X)0color(white)(XX)0" "" "-729
color(white)(xx)|" "color(white)(Xx)9
" "stackrel("—————————————)
color(white)(xx)|color(white)()color(blue)1color(white)(xxx)color(red)9
Six Repeat Steps Four and Five until you can go no farther.
9color(white)(X)|1" "color(white)(X)0color(white)(XX)0" "" "-729
color(white)(xx)|" "color(white)(Xx)9color(white)(XX)81color(white)(XXxx)729
" "stackrel("—————————————)
color(white)(xx)|color(white)()color(blue)1color(white)(xxx)color(red)9color(white)(XX)color(red)81color(white)(XXXXX)color(red)0
Hence, Quotient is x^2+9x+81 and remainder is 0.
