Determine which of the following polynomials | vedclass

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(A) According to the Factor Theorem,$(x - a)$ is a factor of a polynomial $p(x)$ if $p(a) = 0$.Here,the divisor is $(x + 1)$,which can be written as $

Vedclass · Accepted Answer

Yes,it is a factor.

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(A) According to the Factor Theorem,$(x - a)$ is a factor of a polynomial $p(x)$ if $p(a) = 0$.Here,the divisor is $(x + 1)$,which can be written as $(x - (-1))$. So,we set $a = -1$.Let $p(x) = x^{3} + x^{2} + x + 1$.Now,calculate $p(-1)$:$p(-1) = (-1)^{3} + (-1)^{2} + (-1) + 1$$p(-1) = -1 + 1 - 1 + 1$$p(-1) = 0$Since the remainder $p(-1) = 0$,by the Factor Theorem,$(x + 1)$ is a factor of the polynomial $x^{3} + x^{2} + x + 1$.

Determine which of the following polynomials has $(x + 1)$ as a factor: $x^{3} + x^{2} + x + 1$.

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