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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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?

Similar Questions

Find the value of the polynomial $x^{2}-7x+12$ at $x=1$.

Classify the following as a constant,linear,quadratic,or cubic polynomial:
$5t - \sqrt{7}$

Expand $\left(\frac{x}{2}-\frac{2}{5}\right)^{2}$.

Expand $\left(\frac{2x}{3} + \frac{3y}{4}\right)^{2}$.

Factorise $x^{3}-11 x^{2}+20 x+32$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module