To factor a trinomial of the form x^2 + bx + c, you need to find two numbers p and q such that:

1. p * q = c (The product of p and q is equal to c, the constant term)
2. p + q = b (The sum of p and q is equal to b, the coefficient of the middle term)

Here are the steps to do this:

1. Write down the trinomial equation x^2 + bx + c.

2. Identify the coefficients b and c in the equation.

3. List all the factor pairs of c (the constant term).

4. From this list, find the pair of factors that add up to b (the coefficient of the middle term).

5. Once you have found the correct pair of factors, rewrite the middle term of the trinomial as the sum of the terms bx and cx.

6. Factor by grouping. Split the middle term bx into the sum of two terms, ax and cx, and group the terms to get (x^2 + ax) + (cx + c).

7. Factor out the greatest common factor from each group.

8. If factored correctly, you should now have two binomial factors of the form (x + p)(x + q), where p and q are the factors you found in step 4.

Remember, this method works for trinomials where the coefficient of the x^2 term is 1. If the coefficient is not 1, you would need to use a different factoring method, such as the "ac method" or "factor by grouping".