Step 1. Write only the coefficients of #x# in the dividend inside an upside-down division symbol.
#|4" "" "7color(white)(1)-13" "" "-3#
#|color(white)(1)#
#stackrel("—————————————————)#
Step 2. Put the divisor at the left.
#color(red)(7)|4" "" "7color(white)(1)-13" "" "-3#
#color(white)(1)|color(white)(1)#
#" "stackrel("—————————————————)#
Step 3. Drop the first coefficient of the dividend below the division symbol.
#7|4" "" "7color(white)(1)-13" "" "-3#
#color(white)(1)|color(white)(1)#
#" "stackrel("—————————————————)#
#color(white)(1)|color(red)(4)#
Step 4. Multiply the result by the constant, and put the product in the next column.
#7|4" "" "7color(white)(1)-13" "" "-3#
#color(white)(1)|" "" "color(red)(28)#
#" "stackrel("—————————————————)#
#color(white)(1)|4#
Step 5. Add down the column.
#7|4" "" "7color(white)(1)-13" "" "-3#
#color(white)(1)|" "" "28#
#" "stackrel("—————————————————)#
#color(white)(1)|4" "color(white)(1)color(red)(35)#
Step 6. Repeat Steps 4 and 5 until you can go no farther.
#7|4" "" "7color(white)(1)-13" "" "-3#
#color(white)(1)|" "" "28" "color(white)(1)245" "color(white)(1)1624#
#" "stackrel("—————————————————)#
#color(blue)(color(white)(1)|4" "color(white)(1)35" "color(white)(1)232)" "color(white)(1)color(red)(1621)#
#(4x^3+7x^2-13x-3)/(x-7) = 4x^2+35x+232+1621/(x-7)#
Check:
#(x-7)(4x^2+35x+232+1621/(x-7)) = (x-7)(4x^2+35x+232)-1621 = 4x^3+35x^2+232x-28x^2-245x-1624+1621#
#= 4x^3+7x^2-13x-3#
