"simple" polynomial question, any help would be appreciated
Show that (x-1)(x-2) is a factor of
P(x) = x^n (2^m -1) + x^m(1-2^n) + (2^n - 2^m)
m and n are positive integers
Well if the expressions and are factors of the given polynomial, and must be its roots.
So just substitute and then and see if the equation
is satisfied.
so for , the value of the polynomial is,
Hence the above equation is satisfied. So x-1 is a factor.
Now, insert and prove that the value of the polynomial becomes zero.
so as x=1 and x=2 are the roots of the given polynomial is a factor.