How do you use polynomial synthetic division to divide #(2x^3+x^2+2x+1)div(x+1/2)# and write the polynomial in the form #p(x)=d(x)q(x)+r(x)#?

1 Answer
Aug 7, 2017

Answer:

The answer is #=(2x^2+2)(x+1/2)#

Explanation:

Let's perform the synthetic division

#color(white)(aaaa)##-1/2##color(white)(aaaa)##|##color(white)(aa)##2##color(white)(aaaaaaa)##1##color(white)(aaaaaa)##2##color(white)(aaaaaaa)##1#
#color(white)(aaaaaaaaaaaa)##------------#

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aaaa)##color(white)(aaaaa)##-1##color(white)(aaaaaa)##0##color(white)(aaaaa)##-1#
#color(white)(aaaaaaaaaaaa)##------------#

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aaa)##2##color(white)(aaaaaaa)##0##color(white)(aaaaaa)##2##color(white)(aaaaaa)##color(red)(0)#

The remainder is #color(red)(0)# and the quotient is #=2x^2+2#

Therefore,

#(2x^3+x^2+2x+1)=(2x^2+2)(x+1/2)#