The answer is no.
Explanation #1
Define the numerator as
f(x) = x^2 - 5x + 7.
If (x-9) is a factor, then x=9 will be a zero of f(x), so that f(9)=0.
f(9) = 9^2 - 5*9 + 7 = 43
Because f(9)≠0, (x-9) is not a factor of f(x).
Explanation #2
Perform long division.
x + 4
-------------------------
x-9 | x^2 - 5x + 7
x^2 - 9x
----------------------
4x + 7
4x - 36
-----------
43
Because there is a remainder of 43, the numerator cannot be factored with (x-9) as a factor.