Examine the validity of the statement: (x+3) | vedclass

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

Question

(A) To check if $(x+3)$ is a factor of $p(x) = x^{3}+6x^{2}+5x-12$,we use the Factor Theorem.According to the Factor Theorem,$(x-a)$ is a factor of $p

Vedclass · Accepted Answer

True

Vedclass · Answer

(A) To check if $(x+3)$ is a factor of $p(x) = x^{3}+6x^{2}+5x-12$,we use the Factor Theorem.According to the Factor Theorem,$(x-a)$ is a factor of $p(x)$ if $p(a) = 0$.Here,$x+3 = x-(-3)$,so we need to evaluate $p(-3)$.$p(-3) = (-3)^{3} + 6(-3)^{2} + 5(-3) - 12$$p(-3) = -27 + 6(9) - 15 - 12$$p(-3) = -27 + 54 - 15 - 12$$p(-3) = 54 - 54 = 0$.Since $p(-3) = 0$,$(x+3)$ is indeed a factor of the given polynomial.Therefore,the statement is True.

Examine the validity of the statement: $(x+3)$ is a factor of $x^{3}+6x^{2}+5x-12$.

Similar Questions

The graph of $p(x) = -x^2 + x + 6$ is a.........

The graph of linear polynomial $p(x) = 3x - 6$ intersects the $X$-axis at $\ldots......$

Find the zeroes of the following polynomial by the factorisation method and verify the relationship between the zeroes and the coefficients of the polynomial: $4x^2 - 3x - 1$

Obtain the value of the following polynomial at the given values of $x$: $p(x) = 10 - 5x + 3x^2 - x^3$; at $x = 2$ and $x = -2$.

Find $k$ such that $x^{2}+2x+k$ is a factor of $2x^{4}+x^{3}-14x^{2}+5x+6$. Also,find all the zeroes of the two polynomials.

Vedclass Test Series

Exam Paper Generator

Online Exam Module