Question

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

Answer 1

Given that, the polynomial x³-2mx²+16 is divisible by x+2

So, x+2 must be the factor of given polynomial

x+2=0

x=-2

So, -2 is the zero of given polynomial

x³-2mx²+16 = 0

Replacing x by -2

(-2)³-2m(-2)²+16 = 0 

-8-8m+16 = 0

Taking -8 as common and passed to RHS

-8(1+m-2) = 0

1+m-2 = 0

m-1 = 0

m=1

therefore, the value of m in the given polynomial is 1