Examine the validity of the following stateme | vedclass

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

Question

(B) To check if $(x-2)$ is a factor of the polynomial $p(x) = x^{3}+5x^{2}-2x-25$,we use the Factor Theorem.According to the Factor Theorem,$(x-a)$ is

Vedclass · Accepted Answer

False

Vedclass · Answer

(B) To check if $(x-2)$ is a factor of the polynomial $p(x) = x^{3}+5x^{2}-2x-25$,we use the Factor Theorem.According to the Factor Theorem,$(x-a)$ is a factor of $p(x)$ if and only if $p(a) = 0$.Here,$a = 2$.Substitute $x = 2$ into the polynomial:$p(2) = (2)^{3} + 5(2)^{2} - 2(2) - 25$$p(2) = 8 + 5(4) - 4 - 25$$p(2) = 8 + 20 - 4 - 25$$p(2) = 28 - 29$$p(2) = -1$Since $p(2) 
eq 0$,$(x-2)$ is not a factor of the given polynomial.Therefore,the statement is False.

Examine the validity of the following statement: $(x-2)$ is a factor of $x^{3}+5x^{2}-2x-25$.

Similar Questions

From the following figure,find the number of zeros of $y=p(x)$ :

The zeroes of the quadratic polynomial $x^{2}+99x+127$ are

The product of two polynomials is $3x^3 - x^2 - 3x + 1$ and one of the polynomials is $3x^2 + 2x - 1$. Find the other polynomial.

Are the following statements 'True' or 'False'? Justify your answers.
If the graph of a polynomial intersects the $x$-axis at exactly two points,it need not be a quadratic polynomial.

The zeros of cubic polynomial $p(x) = ax^3 + bx^2 + cx + d$; $a \neq 0, a, b, c, d \in R$ are $\alpha, \beta$ and $\gamma$; then $\alpha\beta + \beta\gamma + \gamma\alpha = \ldots$

Vedclass Test Series

Exam Paper Generator

Online Exam Module