Factor the expressions:

x^2 - 13x + 30

x^2 - 13x + 30.

c = 30 = -3*-10.
(x-3)(x-10).

To factor the expression x^2 - 13x + 30, we need to find two numbers that multiply to give 30 and add up to -13x. Let's go step by step to find these numbers:

Step 1: Find the factors of 30
The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30.

Step 2: Determine the correct combination
We are looking for two numbers that multiply to give 30 and add up to -13. After examining the factors, we find that -3 and -10 satisfy these conditions, since (-3) * (-10) = 30 and -3 + (-10) = -13.

Step 3: Write the factored form
Now we can write the factored form of the expression:
x^2 - 13x + 30 = (x - 3)(x - 10).

Thus, the expression x^2 - 13x + 30 can be factored as (x - 3)(x - 10).