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Factor Trinomials by Unfoiling (Trial and Error)

Related Topics: More Algebra Lessons

How to factor trinomials by trial and error or unfoiling?

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

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.


Factor the following trinomial.

x2 - 5x + 6


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)

How to factor trinomials by reverse FOIL (or trial and error method) and Grouping?
Factor ax2 + bx + c where a ≠ 1.
Method 1: Trail and Error (Reverse FOIL)
Step 1: Place the factors of ax2 in the first positions of the 2 sets of parentheses that represent the factors.
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.
1. 6x2 - 19x + 15
2. 15x2 + 17x - 42

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.
3. 9x2 - 15x + 4
2. 10x2 + 7x - 12 How to factor trinomials when the leading coefficient is not equal to 1 using the trial and error method?
Factor using trial and error.
1. 4x2 − 4x − 15
2. 20x2 + 19x + 3

Examples of factoring trinomial by unfoiling (trial and error method)
1. 3x2 − x − 4
2. 6y2 − 48y − 120
3. 5r4 − 7r2s − 6s2
How to factor trinomials by trial and error?
To factor ax2 + bx + c:
• Find 2 first terms whose product is ax2.
• 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.

1. Factor 8x2 − 10x − 3
2. Factor 6x2 + 19x - 7 Factor trinomial, gcf then unfoil
8w2 − 48w + 64 Factoring quadratics trinomials 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.
2x2 + 9x + 4
3x2 - x - 2
12x2 - 11x + 2 This trinomial calculator will help you to factorize trinomials. It will also plot the graph.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
Mathway Calculator Widget

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