From the following polynomials,find out which | vedclass

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

Question

(A) To determine if $(x+1)$ is a factor of the polynomial $p(x) = x^{3} + 10x^{2} + 23x + 14$,we use the Factor Theorem.According to the Factor Theore

Vedclass · Accepted Answer

Yes

Vedclass · Answer

(A) To determine if $(x+1)$ is a factor of the polynomial $p(x) = x^{3} + 10x^{2} + 23x + 14$,we use the Factor Theorem.According to the Factor Theorem,$(x+1)$ is a factor of $p(x)$ if $p(-1) = 0$.Substitute $x = -1$ into the polynomial:$p(-1) = (-1)^{3} + 10(-1)^{2} + 23(-1) + 14$$p(-1) = -1 + 10(1) - 23 + 14$$p(-1) = -1 + 10 - 23 + 14$$p(-1) = 9 - 23 + 14$$p(-1) = -14 + 14 = 0$Since $p(-1) = 0$,$(x+1)$ is indeed a factor of the given polynomial.

From the following polynomials,find out which of them has $(x+1)$ as a factor:
$x^{3} + 10x^{2} + 23x + 14$

Similar Questions

Which of the following expressions is a polynomial? State the reason. If an expression is a polynomial,state whether it is a polynomial in one variable or not: $\sqrt{3} x^{2}+\pi x-9$

Expand $(3x - 2)(3x - 6)$.

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

By the Remainder Theorem,find the remainder when $p(x)$ is divided by $g(x)$,where $p(x) = x^{3} - 3x^{2} + 4x + 50$ and $g(x) = x - 3$.

Verify whether the following is True or False:
$-3$ is a zero of $x-3$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module

From the following polynomials,find out which of them has $(x+1)$ as a factor:$x^{3} + 10x^{2} + 23x + 14$