(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)
