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Factor trinomials

Introduction to factor trinomials

You can factor trinomials by the methods of "splitting the middle term" and "factoring by grouping". Let us discuss in detail along with an example how to factor trinomials. This will help you understand the exact method and steps to factor trinomials.

Factor trinomials by followng these three steps in general:

  1. Convert the trinomial to its standard form
  2. Split the middle term
  3. Factor by grouping

By following the above three steps you will be able to factor trinomials that are quadratic in nature. Let us now take an example to see how the above three methods factor trinomials:

Steps to factor trinomials

Consider the trinomial 3x2 + 2 + 5x. In order to factor it, we will follow the above three steps:

Step 1: Convert the trinomial to its standard form
In the standard form, you have to write the squared term first, then the term with a variable without an exponent, and then the constant number of the trinomial. For example, the above mentioned trinomial will be written as follows:
3x2 + 5x + 2
Step 2: Split the middle term
In short, when you split the middle term of a trinomial, you have to get two terms (negative or positive), which, on adding give the middle term of the trinomial, and which, on multiplying produce the result equal to the master product of the trinomial.
The master product of a trinomial is the product of the first and third terms of a trinomial. 
The master product of the given trinomial is 6x2, thus we can split the middle term into two parts 6x and -x, because on adding them, we get the middle term 5x, and on mulitplying them, we get the master product 6x2. Thus we can rewrite the expression as:
6x2 + 6x - x + 2
Step 3: Factor by grouping
In this step, you have to make two groups of the expression obtained in the last step. One group should contain the first two terms and the other group should contain the last two terms of the expression. Then you have to take the highest common factor out of each two groups.
3x(x + 1) + 1(x + 1) = (3x + 1)(x + 1)
Thus the trinomial was factored by splitting the middle term.

Conclusion of factor trinomials

It is clear that to factor trinomials, you have to rewrite it in descending order of its exponents, and then split the middle term. After splitting the middle term, the trinomial gets converted into a four termed algebraic expression, which can be factored by grouping in order to completely factor the trinomial.

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