Explain the process of factoring a trinomial.

To factor a trinomial, we need to find two binomials that multiply to give the trinomial.

First, we need to check if the trinomial is in the form of ax^2 + bx + c. If it is, we can use the following steps:

1. Find the factors of a and c.
2. Look for two factors that add up to b.
3. Rewrite the trinomial as the sum of two binomials using the factors found in step 1 and 2.
4. Factor out any common factors from the two binomials.

For example, let's factor the trinomial 2x^2 + 7x + 3.

1. The factors of 2 are 1 and 2, and the factors of 3 are 1 and 3.
2. We need to find two factors that add up to 7. The only pair that works is 2 and 5.
3. Rewrite the trinomial as (2x^2 + 2x) + (5x + 3).
4. Factor out 2x from the first binomial and 1 from the second binomial to get 2x(x + 1) + 1(5x + 3).
5. The final answer is (2x + 1)(x + 3).

If the trinomial is not in the form of ax^2 + bx + c, we may need to use other methods such as grouping or the quadratic formula.