# Factor Trinomials by Unfoiling (Trail and Error)

Another method that we can use to factor trinomials is by trail and error or unfoiling.

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

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)

## Videos

The following videos show many examples of factoring trinomial by trial and error.

Factor trinomial by unfoiling (trial and error)

4x

^{2} + 15x + 9

Factor trinomial by unfoiling (trial and error)

4x

^{2} − 15x + 9

Factor trinomial by unfoiling (trial and error)

20x

^{2} − 13x −15

Factor trinomials by GCF and the unfoiling (trial and error)

Factor trinomial, gcf then unfoil

−7a

^{2} −50ab −7b

^{2}
Factor trinomial, gcf then unfoil

8w

^{2} − 48w + 64

Factor trinomial, gcf then unfoil

a

^{4} + 6a

^{3}b
− 7a

^{2}b

^{2}
Factor trinomial, large coefficients, gcf then unfoil

120x

^{4} +50x

^{3} − 125x

^{2}
This trinomial calculator will help you to factorize trinomials. It will also plot the graph.

You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.