Question

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

Answer 1

Answer:

Step-by-step explanation

Let p(x) = x^3 - 2mx^2 + 16

Let f(x) = x+2

If p(x) is divisible by f(x) then the remainder should ve equal to zero

Applying the remainder theorem

x + 2 =0

=>x = -2

Now I since the remainder is zero, so

p(-2) = 0

=>(-2)^3 -2m × (-2)^2 +16 = 0

=>-8 -8m + 16 = 0

-8m + 8 = 0

-8m = -8

m =8/8

m = 1

Hope it is clear

Answer 2

Answer:

m=1

Step-by-step explanation:

Let p(x) = x3 -2mx2 +16

Since, p(x) is divisible by (x+2), then remainder = 0

P(-2) = 0

⇒ (-2)3 -2m(-2)2 + 16=0

⇒ -8-8m+16=0

⇒ 8 = 8 m

m = 1

Hence, the value of m is 1 .