To divide f(2) for 5x^3+18x^2+7x-6 by x+3
One Write the coefficients of x in the dividend inside an upside-down division symbol.
color(white)(1)|color(white)(X)5" "color(white)(X)18color(white)(XX)+7" "" "-6
color(white)(1)|" "color(white)(X)
" "stackrel("—————————————)
Two Put -3 in the divisor at the left as x+3=0 gives x=-3
-3|color(white)(X)5" "color(white)(X)18color(white)(XX)7" "" "-6
color(white)(xx)|" "color(white)(X)
" "stackrel("—————————————)
Three Drop the first coefficient of the dividend below the division symbol.
-3|color(white)(X)5" "color(white)(X)18color(white)(XX)7" "" "-6
color(white)(xx)|" "color(white)(X)
" "stackrel("—————————————)
" "color(white)(1)|color(white)(X)color(red)
Four Multiply the result by the constant, and put the product in the next column.
-3|color(white)(X)5" "color(white)(X)18color(white)(XX)7" "" "-6
color(white)(xx)|" "color(white)(X)
" "stackrel("—————————————)
" "color(white)(1)|color(white)(X)color(blue)5
Five Add down the column.
-3|color(white)(X)5" "color(white)(X)18color(white)(XX)7" "" "-6
" "color(white)(1)|" "color(white)(X)-15
color(white)(1)stackrel("—————————————)
color(white)(xx)|color(white)(X)color(blue)5color(white)(XXX)color(red)3
Six Repeat Steps Four and Five until you can go no farther.
-3|color(white)(X)5" "color(white)(X)18color(white)(XX)7" "" "-6
" "color(white)(1)|" "color(white)(X)-15color(white)(X)-9color(white)(XXX)6
color(white)(1)stackrel("—————————————)
color(white)(xx)|color(white)(X)color(blue)5color(white)(XXX)color(red)3color(white)(X)color(red)-2color(white)(XXX)color(red)0
Hence remainder is 0 and quotient is 5x^2+3x-2
