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 $6x^2 + 17x + 5$ by splitting the middle term,and by using the Factor Theorem.

Factorise $y^2 - 5y + 6$ by using the Factor Theorem.

Factorise the following: $8a^3 - b^3 - 12a^2b + 6ab^2$

Factorise: $12 x^{2}-7 x+1$

Evaluate using suitable identities: $(104)^{3}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module