To factor the quadratic expression \(2f^2 - 9f + 9\), we can use the method of factoring by grouping or the quadratic formula to find the roots, and then express the quadratic in its factored form.
First, let's see if we can find two numbers that multiply to \(ac = 2 \times 9 = 18\) (where \(a = 2\) and \(c = 9\)) and add to \(b = -9\). We need to find two numbers that multiply to 18 and add to -9. The suitable pair is \(-6\) and \(-3\).
Now we can rewrite the middle term, \(-9f\), using those two numbers:
\[ 2f^2 - 6f - 3f + 9 \]
Now, we group the terms:
\[ (2f^2 - 6f) + (-3f + 9) \]
Factoring out the greatest common factors in each group gives:
\[ 2f(f - 3) - 3(f - 3) \]
Now, we can factor out \((f - 3)\):
\[ (2f - 3)(f - 3) \]
So the completely factored form of the expression \(2f^2 - 9f + 9\) is:
\[ \boxed{(2f - 3)(f - 3)} \]