Question

For what value of ′m ′  is x3−2mx2+15 divisible by x−1?​

Answer 1

Answer:

The value of m is 1.

Step-by-step explanation:

Given the polynomial}x^3-2mx^2+16Given the polynomial x3−2mx2+16

we have to find the value of m for which given polynomial is divisible by x+2 we have to find the value of m for which given polynomial is divisible byx+2

P(x)=x^3-2mx^2+16P(x)=x3−2mx2+16

when the above polynomial is divisible is x+2 then the remainder will be 0.

By remainder theorem

P(-2)=0P(−2)=0

(-2)^3-2m(-2)^2+16=0(−2)3−2m(−2)2+16=0

-8-8m+16=0−8−8m+16=0

8m=88m=8

Divide throughout the equation by 8

m=\frac{8}{8}=1m=88=1

Hence, the value of m is 1.