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

1 Answer
Feb 21, 2017

Answer:

The remainder is #=49/8# and the quotient is #=3x^2+1/2x+3/4#

Explanation:

We perform the synthetic division

#color(white)(aaaa)##3/2##color(white)(aaaa)##|##color(white)(aaaa)##3##color(white)(aaaa)##-4##color(white)(aaaaa)##0##color(white)(aaaaaa)##5#

#color(white)(aaaaaa)##color(white)(aaaa)##|##color(white)(aaa)##color(white)(aaaaaaaa)##9/2##color(white)(aaaa)##3/4##color(white)(aaaa)##9/8#

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

#color(white)(aaaa)##color(white)(aaaaaa)##color(white)(aaaaaa)##3##color(white)(aaaaa)##1/2##color(white)(aaaaa)##3/4##color(white)(aaaaa)##color(red)(49/8)#

The remainder is #=49/8#

The quotient is #=3x^2+1/2x+3/4#

Verification, by using the remainder theorem

#f(3/2)=81/8-9+5=81/8-4=49/8#