How to factor trinomials


Trinomials are algebraic expressions made up of three terms. Tri means three and nomials means name or term. Factoring means to write in a simpler or the simplest form. Thus, how to factor trinomials explains a procedure of how to rewrite three termed algebraic expressions in simplest form.

The answer to "How to factor trinomials?" is that you have to split the middle term of a trinomial and then rewrite the trinomial as a product of two algebraic expressions. This is called factoring trinomials. For example, the following trinomial:
3x2 - 14x
can be factored into this expression:
(x + 4)(x - 2)
The following article teaches you on how to factor trinomials:

Step by step method of how to factor trinomials

Let us take the example of the following trinomial in order to learn how to factor trinomials:
x2 + 2x - 8
The following are the steps on how to facto trinomials:

Step 1: Identify the middle term of the trinomial. Here the middle term is 2x

Step 2: Split the middle term into two parts - which add to give the middle term itself. For example, in the above trinomial, the middle term is split as 2x = 4x - 2x
Therefore we can rewrite the trinomial as
x2 + 4x - 2x - 8
Step 3: Group the four terms into two groups, with the first two terms forming one group and the next two terms forming the other group. Then take the highest common factor out of each group as follows:
x(x + 4) - 2(x + 4)
Step 4: Now if you have done the steps properly till now, you will have a common expression in both the groups. Here the common expression is (x + 4). Factor out the common expression as follows:
(x + 4)(x - 2)
Therefore you have factored the trinomial and as a result rewritten as a product of two binomials. This is how to factor trinomials.

Conclusion on how to factor trinomials

This article on "How to factor trinomials" has explained you the step by step method of factoring a trinomial with the help of the method of splitting the middle term.

In order to practice how to factor trinomials, you can factor the following trinomials:

  • 2x2 + 4x - 6
  • 3x2 + 4x + 1
  • 5x2 + 3x - 2

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