Question

Determine which of the following polynomials has
(x + 1)a factor :

(i) x^3+ x^2+ x + 1​

Answer 1

Step-by-step explanation:

(i) x³+x²+x+1

Let p(x)= x³+x²+x+1

The zero of x+1 is -1.

On putting x= -1

p(−1)=(−1)³+(−1)²+(−1)+1

=−1+1−1+1=0

Hence, by factor theorem, x+1 is a factor of x³+x²+x+1

Hope it helps!