To factor the expression \( 9 - 6x + x^2 \), we first rewrite it in standard form:
\[ x^2 - 6x + 9 \]
Next, we look for two numbers that multiply to \( 9 \) (the constant term) and add to \( -6 \) (the coefficient of the linear term). The numbers that satisfy these conditions are \( -3 \) and \( -3 \).
Thus, we can express the quadratic as:
\[ x^2 - 3x - 3x + 9 = (x - 3)(x - 3) = (x - 3)^2 \]
Therefore, we can factor the original expression as:
\[ 9 - 6x + x^2 = (x - 3)^2 \]
In conclusion, the factored form of the expression is:
\[ \boxed{(x - 3)^2} \]