How do you divide using synthetic division: #(2x^3 - 4x^2 - 7x + 5)/(x - 3)#?

1 Answer
Feb 21, 2017

Answer:

The remainder is #=2# and the quotient is #=2x^2+2x-1#

Explanation:

We perform the synthetic division

#color(white)(aaaa)##3##color(white)(aaaa)##|##color(white)(aaaa)##2##color(white)(aaaa)##-4##color(white)(aaaaa)##-7##color(white)(aaa)##5#

#color(white)(aaaaaa)##color(white)(aaa)##|##color(white)(aaa)##color(white)(aaaaaaaa)##6##color(white)(aaaaaa)##6##color(white)(aaa)##-3#

#color(white)(aaaaaaaaaa)#------------------------------------------------------------

#color(white)(aaaa)##color(white)(aaaaaa)##color(white)(aaaaaa)##2##color(white)(aaaa)##2##color(white)(aaaaa)##-1##color(white)(aaaaa)##color(red)(2)#

The remainder is #=2#

The quotient is #=2x^2+2x-1#

Verification, by using the remainder theorem

#f(3)=54-36-21+5=59-57=2#