(Division format from Ernest Z. here on Socratic)
Step 1. Write only the coefficients of #x# in the dividend inside an upside-down division symbol.
#color(white)(1)|1" "-2color(white)(XX)5" "" "-6#
#color(white)(1)|" "color(white)(X)#
#" "stackrel("—————————————)#
Step 2. Put the constant in the divisor #x-c# at the left. In this case #c=3#
#3|1" "-2color(white)(XX)5" "" "-6#
#color(white)(1)|" "color(white)(X)#
#" "stackrel("—————————————)#
Step 3. Drop the first coefficient of the dividend below the division symbol.
#3|1" "-2color(white)(XX)5" "" "-6#
#color(white)(1)|" "color(white)(X)#
#" "stackrel("—————————————)#
#color(white)(1)|1#
Step 4. Multiply the result by the constant, and put the product in the next column.
#3|1" "-2color(white)(XX)5" "" "-6#
#color(white)(1)|" "color(white)(X1)3#
#" "stackrel("—————————————)#
#color(white)(1)|1#
Step 5. Add down the column.
#3|1" "-2color(white)(XX)5" "" "-6#
#color(white)(1)|" "color(white)(X1)3" "#
#" "stackrel("—————————————)#
#color(white)(1)|1" "" "1#
Step 6. Repeat Steps 4 and 5 until you can go no farther.
#3|1" "-2color(white)(XX)5" "color(white)(1)-6#
#color(white)(1)|" "color(white)(X1)3" "color(white)(X1)3color(white)(XX1)24#
#" "stackrel("—————————————)#
#color(white)(1)|1" "color(white)(X)1" "color(white)(X1)8" ""|"color(white)(X1)18#
The remainder is #18#
(And the quotient is #1x^2+1x+8#, more commonly written #x^2+x+8#)
