x+1 is a factor of which of the following pol | vedclass

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(B) According to the Factor Theorem,if $(x+1)$ is a factor of a polynomial $p(x)$,then $p(-1)$ must be equal to $0$.$(a)$ Let $p(x) = x^{3}+x^{2}-x+1$

Vedclass · Accepted Answer

$x^{3}+x^{2}+x+1$

Vedclass · Answer

(B) According to the Factor Theorem,if $(x+1)$ is a factor of a polynomial $p(x)$,then $p(-1)$ must be equal to $0$.$(a)$ Let $p(x) = x^{3}+x^{2}-x+1$.$p(-1) = (-1)^{3}+(-1)^{2}-(-1)+1 = -1+1+1+1 = 2 
eq 0$.So,$(x+1)$ is not a factor.$(b)$ Let $p(x) = x^{3}+x^{2}+x+1$.$p(-1) = (-1)^{3}+(-1)^{2}+(-1)+1 = -1+1-1+1 = 0$.Since $p(-1) = 0$,$(x+1)$ is a factor.$(c)$ Let $p(x) = x^{4}+x^{3}+x^{2}+1$.$p(-1) = (-1)^{4}+(-1)^{3}+(-1)^{2}+1 = 1-1+1+1 = 2 
eq 0$.So,$(x+1)$ is not a factor.$(d)$ Let $p(x) = x^{4}+3x^{3}+3x^{2}+x+1$.$p(-1) = (-1)^{4}+3(-1)^{3}+3(-1)^{2}+(-1)+1 = 1-3+3-1+1 = 1 
eq 0$.So,$(x+1)$ is not a factor.Therefore,$(x+1)$ is a factor of $x^{3}+x^{2}+x+1$. The correct option is $(b)$.

$x+1$ is a factor of which of the following polynomials?

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