Simplifying trinomials involves rewriting them in a simpler form, often by factoring. To factor a trinomial, you typically look for two numbers that multiply to give the constant term and add up to give the coefficient of the middle term. Here’s a step-by-step approach:
-
Identify the trinomial. A trinomial is generally in the form ax² + bx + c.
-
Look for two numbers that multiply to ac (where a is the coefficient of x² and c is the constant term) and add up to b (the coefficient of x).
-
Rewrite the middle term using the two numbers you found. This will break the trinomial into two binomials.
-
Factor by grouping. If you end up with four terms, group them into pairs and factor each pair.
-
Set each factor equal to zero to find the solutions, if applicable.
For example, to simplify the trinomial x² + 5x + 6, you would look for two numbers that multiply to 6 (the constant) and add to 5 (the coefficient of x). The numbers 2 and 3 fit, so you can rewrite the trinomial as (x + 2)(x + 3), which is its simplified factored form.