Question

Determine which of the following polynomials has (x+1) a factor :x^3+x^2+x+1 with long division method​

Answer 1

x+1 is a factor of polynomial x³+x²+x+1  because on dividing x³+x²+x+1 by x+1 there is no remainder left.

according to remainder theorem:

p(x)   =   g(x) × q(x)  +  r(x)

on dividing x³+x²+x+1 by x+1  q(x) =x²+1   and r(x)  =  0

                    x³+x²+x+1  =    x+1 × x²+1  +0

                      x³+x²+x+1  =   x³+x²+x+1

                          LHS =RHS

                       hence proved