To divide #r^2+6r+15# by #r+5#
One Write the coefficients of #t# in the dividend inside an upside-down division symbol.
#color(white)(1)|color(white)(X)1" "color(white)(X)6color(white)(XX)15#
#color(white)(1)|" "color(white)(X)#
#" "stackrel("—————————————)#
Two Put the divisor at the left (as it is #r+5#, we need to put #-5#.
#-5|color(white)(X)1" "color(white)(X)6color(white)(XX)15#
#color(white)(Xx)|" "color(white)(X)#
#" "stackrel("—————————————)#
Three Drop the first coefficient of the dividend below the division symbol.
#-5|color(white)(X)1" "color(white)(X)6color(white)(XX)15#
#color(white)(xx)|" "color(white)(X)#
#" "stackrel("—————————————)#
#color(white)()(1)|color(white)(X)color(red)1#
Four Multiply the result by the constant, and put the product in the next column.
#-5|color(white)(X)1" "color(white)(X)6color(white)(XX)15#
#color(white)(221)|" "color(white)(X)-5#
#" "stackrel("—————————————)#
#color(white)(221)|color(white)(X)color(blue)1#
Five Add down the column.
#-5|color(white)(X)1" "color(white)(X)6color(white)(XX)15#
#color(white)(221)|" "color(white)(X1)-5#
#" "stackrel("—————————————)#
#color(white)(221)|color(white)(X)color(blue)1color(white)(XX)color(red)1#
Six Repeat Steps Four and Five until you can go no farther.
#2|color(white)(X)1" "color(white)(X)6color(white)(XX)15#
#color(white)(1)|" "color(white)(X1)-5color(white)(X)-5#
#" "stackrel("—————————————)#
#color(white)(1)|color(white)(X)color(blue)1color(white)(X11)color(red)1color(white)(XX)color(red)10#
Remainder is #10# and
#(r^2+6r+15)-:(r+5)=r+1+10/(r+5)#
