Respuesta :

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.

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