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

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

Answers (1)

m = 1

Solution

Given : x^{3}-2mx^{2}+16  is divisible by x+2

We know that if (x+a)  is factor of the polynomial f(x), then it always satisfies f(-a)=0

If x^{3}-2mx^{2}+16  is divisible by x+2  then according to remainder theorem if we put x=-2  in the polynomial x^{3}-2mx^{2}+16  then the output must be equal to 0.

Let x^{3}-2mx^{2}+16
Put       x=-2

\\p(-2)=(-2)^{3}-2m(-2)^{2}+16\\ 0=-8-8m+16\\ 0=-8m+8\\ 8m=8\\ m=\frac{8}{8}=1\\

Hence, m=1

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