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Factor Trinomials by Unfoiling (Trail and Error)




 

One of the methods 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 the trial and error method. Many examples and worked solutions are shown.
It is also possible to factorize 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.

x2 - 5x + 6

Solution:

Step 1:The first term is x2, which is the product of x and x. Therefore, the first term in each bracket must be x, i.e.

x2 - 5x + 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 -5x as the middle term is (x - 3)(x - 2)

Step 3: The answer is then

x2 - 5x + 6 = (x - 3 )(x - 2)




Videos

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

Factor trinomial by unfoiling (trial and error)
4x2 + 15x + 9
Factor trinomial by unfoiling (trial and error)
4x2 − 15x + 9


 
Factor trinomial by unfoiling (trial and error)
20x2 − 13x −15
Factor trinomials by GCF and the unfoiling (trial and error)
Factor trinomial, gcf then unfoil
−7a2 −50ab −7b2


Factor trinomial, gcf then unfoil
8w2 − 48w + 64
Factor trinomial, gcf then unfoil
a4 + 6a3b − 7a2b2


 
Factor trinomial, large coefficients, gcf then unfoil
120x4 +50x3 − 125x2
This trinomial calculator will help you to factorize trinomials. It will also plot the graph.

Factoring quadratics without trial and error
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:
2x2 + 9x + 4
3x2 - x - 2
12x2 - 11x + 2

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 widget 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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