Examine the validity of the following stateme | vedclass

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(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

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False

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(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 $x^{3}+5x^{2}-2x-25$.

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