Question

determine which of the following polynomials has (x+1) a factor: xcube+xsquare+x+1​

Answer 1

x+1=0

X=0-1

x=-1

$( { - 1})^{3} +( { - 1})^{2} + ( - 1) + 1$

-1+1-1+1

=0

so,x+1 is the factor of given polynomial

Answer 2

p(x) = x³ + x² + x + 1

If x+1 is the factor of p(x), then - 1 is the zero of p(x).

p(x) = x³ + x² + x + 1

p(-1) = (-1)³ + (-1)² + (-1) +1

0 = - 1 + 1 - 1 +1

0 =0

Therefore, x+1 is the factor of x³ + x² + x + 1.