One of the methods that we can use to factor trinomials is by trial and error or unfoiling.

In these lessons, we will learn how to factorize trinomials by the trial and error method. Many examples and worked solutions are shown.

It is also possible to factorize quadratic trinomials without trial and error. This is shown in the last video on this page.

We also have a trinomial calculator that will help you to factorize trinomials. Use it to check your answers.

Related Topics: More Algebra Lessons

*Example: *

Factor the following trinomial.

*x*^{2} - 5*x* + 6

*Solution*:

**Step 1:**The first term is *x*^{2}*, *which is the product of *x* and *x*. Therefore, the first term in each bracket must be *x*, i.e.

*x*^{2} - 5*x* + 6 = (*x *... )(*x *... )

**Step 2**: The last term is 6. The possible factors are ±1 and ±6 or ±2 and ±3. So, we have the following choices.

(*x* + 1)(*x* + 6)

(*x* - 1)(*x* - 6)

(*x* + 3)(*x* + 2)

(*x* - 3 )(*x* - 2)

The only pair of factors which gives -5*x* as the middle term is (*x* - 3)(*x* - 2)

**Step 3:** The answer is then

*x*^{2} - 5*x* + 6* = *(*x* - 3 )(*x* - 2)

Factor ax

Method 1: Trail and Error (Reverse FOIL)

Step 1: Place the factors of ax

Step 2: Place 2 possible factors of c into the second positions of the parentheses.

Step 3: Find the inner and outer products of the 2 sets of parentheses.

Step 4: Keep trying different factors until the inner and outer products add to bx.

Examples:

Factor

1. 6x

2. 15x

Method 2: Grouping

Step 1: Find the product ac.

Step 2: Find the factors of ac that add to b.

Step 3: Rewrite bx as a sum or difference of the factors of ac that add to b.

Step 4: The trinomial should now consist of 4 terms. Factor by grouping.

Examples:

Factor

3. 9x

2. 10x

Example:

Factor using trial and error.

1. 4x

2. 20x

Examples:

1. 3x

2. 6y

3. 5r

To factor ax

• Find 2 first terms whose product is ax

• Find 2 last terms whose product is c.

• Use trial and error until the sum of the ouside product and the inside product is bx.

Example:

1. Factor 8x

2. Factor 6x

Example:

8w

This video shows a quick method for factoring quadratic expressions where the coefficient of the x squared term is not 1. This is a quick method that allows the correct answer to be achieved without trial and error and guess work.

Examples:

2x

3x

12x

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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