Is x+1 a factor of 4x^3 + 7x^2 - 2x - 5 or no | 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 $p(x) = 4x^3 + 7x^2 - 2x - 5$,we use the Factor Theorem.According to the Factor Theorem,$(x-

Vedclass · Accepted Answer

Yes

Vedclass · Answer

(A) To determine if $(x+1)$ is a factor of the polynomial $p(x) = 4x^3 + 7x^2 - 2x - 5$,we use the Factor Theorem.According to the Factor Theorem,$(x-a)$ is a factor of $p(x)$ if $p(a) = 0$.Here,we set $x+1 = 0$,which gives $x = -1$.Now,we calculate $p(-1)$:$p(-1) = 4(-1)^3 + 7(-1)^2 - 2(-1) - 5$$p(-1) = 4(-1) + 7(1) + 2 - 5$$p(-1) = -4 + 7 + 2 - 5$$p(-1) = 0$Since $p(-1) = 0$,$(x+1)$ is indeed a factor of the given polynomial.

Is $x+1$ a factor of $4x^3 + 7x^2 - 2x - 5$ or not?

Similar Questions

If $x^{51} + 51$ is divided by $x + 1$,the remainder is

If $p(-3)=0,$ then one of the factors of $p(x)$ is.........

Which of the following expressions are polynomials in one variable and which are not? State the reason for your answer. If the given expression is a polynomial,state whether it is a polynomial in one variable or not.
$x^{2} + x - 3 + \frac{4}{x}$

Find the quotient and the remainder when $x^{3}+x^{2}-10x+8$ is divided by $x+4$.

Write the degree of the following polynomial: $\sqrt{11} t+14$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module