How do you divide #(3x^3+4x^2+2x+5)/(x-4)# ?

1 Answer
Jul 10, 2018

The remainder is #269# and the quotient is #=3x^2+16x+66#

Explanation:

Let's perform the synthetic division

#color(white)(aaaa)##4##|##color(white)(aaaa)##3##color(white)(aaaa)##4##color(white)(aaaaaa)##2##color(white)(aaaaaaa)##5#

#color(white)(aaaaa)##|##color(white)(aaaa)##color(white)(aaaaa)##12##color(white)(aaaaa)##64##color(white)(aaaaa)##264#

#color(white)(aaaaaaaaa)###_________

#color(white)(aaaaa)##|##color(white)(aaaa)##3##color(white)(aaaa)##16##color(white)(aaaaa)##66##color(white)(aaaaaa)##color(red)(269)#

The remainder is #269# and the quotient is #=3x^2+16x+66#

#(3x^3+4x^2+2x+5)/(x-4)=(3x^2+16x+66)+(269)/(x-4)#