Question

using remainder theorem, find the remainder when x^3+3x^2+3x+1 is divided by( x+1/2)

Answer 1

x+1/2=0

x=-1/2

Now :

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

=-1/8+3/4-3/2+1

=(-1+6-12+8)/8

=(14-13)/8

=1/8

The remainder is 1/8.