How do you long divide # ( (t^3) - (6t^2) + (1) ) div (t +2) #?

1 Answer
Mar 24, 2017

#t^2-8t+16# and remainder#-31#

Explanation:

# color(white)(aaaaaaaaaa)##color(blue)(t^2-8t+16#
#color(white)(aaaaaaaaaa)##-----#
#color(white)(aaaa)t+2##|##t^3-6t^2+0+1 ### # ###
#color(white)(aaaaaaaaaa)##t^3+2t^2##color(white)#
#color(white)(aaaaaaaaaa)##----#
#color(white)(aaaaaaaaaa)##0-8t^2+0#
#color(white)(aaaaaaaaaaaa)##-8t^2-16t#
#color(white)(aaaaaaaaaaaaa)##----#
#color(white)(aaaaaaaaaaaaaa)##0+16t+1#
#color(white)(aaaaaaaaaaaaaaaaa)##16t+32#
#color(white)(aaaaaaaaaaaaaaaaaaa)##---#
#color(white)(aaaaaaaaaaaaaaaaaa)##0-31#

The remainder is #color(blue)(=-31# and the quotient is #color(blue)(=t^2-8t+16#