Question

for what value of m is x³-2mx²+16 divisible by x+2?​

Answer 1

F ( - 2) = ( - 2) ³ - 2m( -2²) + 16

0 = - 8 - 8m + 16

0 = 8 - 8m

8m = 8

m = 1 Ans.

Answer 2

If

$x {}^{3} - 2mx {}^{2} + 16$

is divisible by x+2 then x+2 is factor of p(x)

So x=-2

putting x=-2

$( - 2) {}^{3} - 2m( - 2 ){}^{2} + 16 = 0$

$- 8 - 8m + 16 = 0$

$8 - 8m = 0$

$8m = 8$

$m = 1$