If x-2 is a factor of x^m - 3x^m-1 +4x-4,find the value of m.

Explanation:

By Factor Theorem,

(2)^m - 3(2)^(m-1) + 4(2) - 4 = 0.

=> 2^m - 1.5 * 2^m + 4 = 0

=> 4 - 0.5 * 2^m = 0

=> 0.5 * 2^m = 4

=> 2^m = 8

=> m = 3.

Hence the value of m is 3.