How do you find the quotient of #(8c^3+6c-5)div(4c-2)# using long division?

2 Answers
Jun 6, 2017

Answer:

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

Explanation:

Let's perform the long division

#4c-2##color(white)(aaaa)##|##8c^3+0c^2+6c-5##color(white)(aaaa)##|##2c^2+c+2#

#color(white)(aaaaaaaaaaa)##8c^3-4c^2#

#color(white)(aaaaaaaaaaaa)##0+4c^2+6c#

#color(white)(aaaaaaaaaaaaaa)##+4c^2-2c#

#color(white)(aaaaaaaaaaaaaaa)##+0+8c-5#

#color(white)(aaaaaaaaaaaaaaaaaaa)##+8c-4#

#color(white)(aaaaaaaaaaaaaaaaaaaa)##+0-1#

Therefore,

#(8c^3+0c^2+6c-5)/(4c-2)=2c^2+c+2-1/(4c-2)#

Jun 6, 2017

Answer:

#(8c^3 +6c-5) div (4c-2) = 2c^2 +c +2 " rem "1#

or:

#(8c^3 +6c-5) div (4c-2) = 2c^2 +c +2 + (-1)/(4c-2)#

Explanation:

  • In each case, #4c# is divided into the term with the highest power of #c# available.
  • the quotient is multiplied by both terms at the side.
  • change signs to subtract the expressions. (shown in red)

#color(white)(wwwwwwww)2c^2+c+2#
#4c-2 )bar(8c^3 " "+6c-5)larr" "# desc order, no term in #c^2#
#color(white)(www)ul(color(red)(-)8c^3color(red)(+)4c^2)" "larr# subtract
#color(white)(wwwwwwwww)4c^2+6c#
#color(white)(wwn.....ww)color(red)(-)ul(4c^2color(red)(+)2c)#
#color(white)(wwwwwwwwwww)+8c-5#
#color(white)(wwwwwwwwwww)color(red)(-)ul( 8c color(red)(+)4)#
#color(white)(wwwwwwwwwwwwww)-1" "# remainder

#(8c^3 +6c-5) div (4c-2) = 2c^2 +c +2 " rem "1#

or:

#(8c^3 +6c-5) div (4c-2) = 2c^2 +c +2 + (-1)/(4c-2)#