Question

find the remainder when x^3

+3x^2+3x+1is devided by 5+2x

Answer 1

Divisor=5+2x.

To find the zero, 5+2x=0
2x=-5

x=-5/2.

By remainder theorem,

Remainder=p(-5/2)=(-5/2)^3+3(-5/2)^2+3(-5/2)+1

=  -125/8+3*25/4-15/2+1

=  -125/8+75/4-15/2+1

       -125+150-60+8
 =   ---------------------------
                 8

     -27
=  -------
      8