For what value of m, p(x) = (x 3 – 2mx 2 + 16) is divisible by (x + 2)?

Question

Philoid · Accepted Answer

It is given in the question that (x + 2) is a factor of x³ – 2mx² + 16

p (x) = x³ – 2mx² + 16

Now, x + 2 = 0

x = - 2

∴ f (-2) = 0

(- 2)³ – 2m (- 2)² + 16 = 0

- 8 – 8m + 16 = 0

- 8 + 8m = 0

- 8 = - 8m

m =

m = 1

Hence, the value of m = 1