Question

for what m is x^3-2mx^2+16 is divisible by x+2

Answer 1

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Answer 2

Answer:

m = 1

Explanation:

Let p(x) = x³-2mx²+16

It is given that, p(x) is divisible by (x+2) .

By factor theorem ,

(x+2) is a factor of p(x).

Therefore,

p(-2) = 0

=> (-2)³-2m(-2)²+16 = 0

=> -8 -2m × 4 + 16 = 0

=> -8 -8m+16 = 0

=> -8m+8 = 0

=> -8m = -8

=> m = (-8)/(-8)

=> m = 1

Therefore,

m = 1

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