To factor the trinomial $x^2 - 9x + 18$, we need to find two numbers that multiply to give 18 and add up to -9.

1. The product of the constant term (18) is positive, so we need two negative factors that add to -9.
2. The two numbers that satisfy this condition are -3 and -6 because: $-3 \times -6 = 18 \quad \text{and} \quad -3 + -6 = -9.$
3. Therefore, the trinomial can be factored as: $(x - 3)(x - 6).$

So, $x^2 - 9x + 18 = (x - 3)(x - 6)$.

Would you like further explanation or have any questions?

Here are 5 related questions:

1. How do you factor a trinomial when the coefficient of $x^2$ is greater than 1?
2. Can you apply factoring to solve quadratic equations?
3. What is the difference between factoring a trinomial and factoring a binomial?
4. How can the discriminant help in determining if a trinomial is factorable?
5. Can all quadratic expressions be factored?

Tip: Always check your factors by expanding them back to verify your factorization is correct.