Factor the trinomial \(x^2 - 5x + 6\).

Step 1 ：Step 1: Identify a, b, and c from the standard form of quadratic equation \(ax^2 + bx + c\). Here, a=1, b=-5, and c=6.

Step 2 ：Step 2: Find two numbers that add up to -5 (the coefficient of x) and multiply to 6 (the constant term). The numbers are -2 and -3.

Step 3 ：Step 3: Write the trinomial as a product of two binomials using the two numbers found in the previous step. So, \(x^2 - 5x + 6 = (x - 2)(x - 3)\).