Step 1. Write only the coefficients of x in the dividend inside an upside-down division symbol.
|4" "color(white)(1)7color(white)(1)-13" " "-3
|color(white)(1)
stackrel("——————————————)
Step 2. Put the divisor at the left.
color(red)(-3)|4" "color(white)(1)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.
-3|4" "color(white)(1)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.
-3|4" "color(white)(1)7color(white)(1)-13" " "-3
" "color(white)(1)|color(white)(1)color(red)(-12)
" "color(white)(1)stackrel("——————————————)
" "color(white)(1)|4
Step 5. Add down the column.
-3|4" "color(white)(1)7color(white)(1)-13" " "-3
" "color(white)(1)|-12
" "color(white)(1)stackrel("——————————————)
" "color(white)(1)|4color(white)(1)color(red)(-5)
Step 6. Repeat Steps 4 and 5 until you can go no farther.
-3|4" "color(white)(1)7color(white)(1)-13" " "-3
" "color(white)(1)|-12" "color(white)(1)15" "color(white)(1)-6
" "stackrel("——————————————)
color(blue)(" "color(white)(1)|4-5" "" "2)" "color(white)(1)color(red)(-9)
(4x^3+7x^2-13x-3)/(x+3) = 4x^2-5x+2-9/(x+3)
Check:
(x+3)(4x^2-5x+2-9/(x+3)) = (x+3)(4x^2-5x+2)-9
= 4x^3-5x^2+2x+12x^2-15x+6-9 = 4x^3+7x^2-13x-3
