Determine whether (x + 1) is a factor of the | vedclass

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

Question

(B) According to the Factor Theorem,$(x + 1)$ is a factor of $p(x)$ if and only if $p(-1) = 0$.Given $p(x) = x^{4} + x^{3} + x^{2} + x + 1$.Substituti

Vedclass · Accepted Answer

No

Vedclass · Answer

(B) According to the Factor Theorem,$(x + 1)$ is a factor of $p(x)$ if and only if $p(-1) = 0$.Given $p(x) = x^{4} + x^{3} + x^{2} + x + 1$.Substituting $x = -1$ into the polynomial:$p(-1) = (-1)^{4} + (-1)^{3} + (-1)^{2} + (-1) + 1$Calculating each term:$p(-1) = 1 - 1 + 1 - 1 + 1$Simplifying the expression:$p(-1) = 1$Since $p(-1) 
eq 0$,by the Factor Theorem,$(x + 1)$ is not a factor of the given polynomial.

Determine whether $(x + 1)$ is a factor of the polynomial $p(x) = x^{4} + x^{3} + x^{2} + x + 1$.

Similar Questions

Factorise: $3x^{2}-x-4$

Use the Factor Theorem to determine whether $g(x)$ is a factor of $p(x)$ in each of the following cases: $p(x) = 2x^3 + x^2 - 2x - 1$,$g(x) = x + 1$.

Find the zero of the polynomial: $p(x) = 3x$

Evaluate the following product without multiplying directly: $103 \times 107$

Find the degree of the polynomial given: $x^{5}-x^{4}+3$

Vedclass Test Series

Exam Paper Generator

Online Exam Module