How do you use synthetic division to divide #( 2x^3 + 3x^2 + 4 ) / ( 2x + 1 )#?

1 Answer
Jul 11, 2018

Answer:

The remainder is #=(9/2)# and the quotient is #=(x^2+x-1/2)#

Explanation:

Let's perform the synthetic division

Divide by #2#

#color(white)(aaaa)##-1/2##|##color(white)(aaaa)##1##color(white)(aaaa)##+3/2##color(white)(aaaaaa)##0##color(white)(aaaaaa)##2#

#color(white)(aaaaaaaa)##|##color(white)(aaaa)##color(white)(aaaaa)##-1/2##color(white)(aaaaa)##-1/2##color(white)(aaaa)##1/4#

#color(white)(aaaaaaaaa)###_________________________________________________________##

#color(white)(aaaaaaaa)##|##color(white)(aaaa)##1##color(white)(aaaaaa)##1##color(white)(aaaaaa)##-1/2##color(white)(aaaaa)##color(red)(9/4)#

The remainder is #=(9/2)# and the quotient is #=(x^2+x-1/2)#

#(2x^3+3x^2+4)/(2x+1)=(x^2+x-1/2)+(9/4)/(x+1/2)#

#(2x^3+3x^2+4)/(2x+1)=(x^2+x-1/2)+(9/2)/(2x+1)#