How to Simplify Trinomials

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:

  1. Identify the trinomial. A trinomial is generally in the form ax² + bx + c.

  2. Look for two numbers that multiply to ac (where a is the coefficient of and c is the constant term) and add up to b (the coefficient of x).

  3. Rewrite the middle term using the two numbers you found. This will break the trinomial into two binomials.

  4. Factor by grouping. If you end up with four terms, group them into pairs and factor each pair.

  5. 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.

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