Determine which of the following polynomials | vedclass

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

Question

(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.

Vedclass · Answer

(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: $x^{3} + x^{2} + x + 1$.

Similar Questions

Find the remainder when $x^{3}+3x^{2}+3x+1$ is divided by $x-\frac{1}{2}$.

Give possible expressions for the length and breadth of each of the following rectangles,in which their areas are given: $\text{Area} = 35y^2 + 13y - 12$.

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

Evaluate the following product without multiplying directly: $104 \times 96$

Factorise: $49 a^{2}+70 a b+25 b^{2}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module