How do you divide #(2n^3+62n-26n^2+4)div(2n-6)# using synthetic division?

1 Answer
Jun 11, 2017

Answer:

The remainder is #=269# and the quotient is #=n^2+34n+89#

Explanation:

Let's perform the synthetic division

#color(white)(aaaa)##3##color(white)(aaaaa)##|##color(white)(aaaa)##1##color(white)(aaaaaa)##31##color(white)(aaaaaa)##-13##color(white)(aaaaa)##2#
#color(white)(aaaaaaaaaaaa)#_________

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aaaa)##color(white)(aaaaaaa)##3##color(white)(aaaaaaa)##102##color(white)(aaaa)##267#
#color(white)(aaaaaaaaaaaa)#________

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aaaa)##1##color(white)(aaaaaa)##34##color(white)(aaaaaaa)##89##color(white)(aaaa)##color(red)(269)#

The remainder is #=269# and the quotient is #=n^2+34n+89#

#(n^3+31n^2-13n+2)/(n-3)=n^2+34n+89+269/(n-3)#

N.B The numerator and denominator were divided by the common factor #2#