I don't understand how to factor trimonials.
http://www.algebrahelp.com/lessons/factoring/trinomial/
Factoring trinomials can be a bit challenging at first, but once you understand the process, it becomes much easier. I'll explain the steps to factor a trinomial so that you can understand how to do it.
Step 1: Check if there is a common factor
Look for any common factors that can be divided out of all three terms of the trinomial. If you find any, divide each term by the common factor. This step simplifies the trinomial and makes factoring easier.
Step 2: Determine the form of the trinomial
In order to factor a trinomial, you need to determine its form. There are three possible forms:
1. A trinomial of the form x² + bx + c
2. A trinomial of the form ax² + bx + c
3. A trinomial of the form ax² + bx + c, where a ≠ 1
Step 3: Factor the trinomial
Once you have determined the form of the trinomial, use the appropriate factoring method. Here are the methods for each form:
1. For a trinomial of the form x² + bx + c, where the coefficient of x² is 1:
- Look for two numbers, let's call them m and n, which multiply to give c and add up to give b.
- Rewrite the trinomial as (x + m)(x + n).
2. For a trinomial of the form ax² + bx + c, where a is not equal to 1:
- Look for two numbers, let's call them m and n, which multiply to give ac and add up to give b.
- Rewrite the trinomial as (mx + p)(nx + q), where p and q are constants.
3. For a trinomial of the form ax² + bx + c, where a ≠ 1:
- This is a bit more complex and involves the method of decomposition or grouping. I can explain this separately if you need.
Step 4: Verify the factored form
Once you have factored the trinomial, you can verify your answer by multiplying the factors and checking if you obtain the original trinomial.
Practice is the key to becoming proficient at factoring trinomials. Try working through some examples and gradually increase the difficulty level as you gain confidence.