For what value of m is x^{3}-2 m x^{2}+16 div | vedclass

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(A) If $x^{3}-2 m x^{2}+16$ is divisible by $x+2$,then by the Factor Theorem,$x+2$ is a factor of $p(x) = x^{3}-2 m x^{2}+16$.For $x+2$ to be a factor

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$m = 1$

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(A) If $x^{3}-2 m x^{2}+16$ is divisible by $x+2$,then by the Factor Theorem,$x+2$ is a factor of $p(x) = x^{3}-2 m x^{2}+16$.For $x+2$ to be a factor,$p(-2)$ must be equal to $0$.Substituting $x = -2$ into the polynomial:$p(-2) = (-2)^{3} - 2m(-2)^{2} + 16$$p(-2) = -8 - 2m(4) + 16$$p(-2) = -8 - 8m + 16$$p(-2) = 8 - 8m$Setting $p(-2) = 0$:$8 - 8m = 0$$8m = 8$$m = 1$Therefore,for $m = 1$,the polynomial is divisible by $x+2$.

For what value of $m$ is $x^{3}-2 m x^{2}+16$ divisible by $x+2$?

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