(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#)