Factoring Trinomials Worksheet Library

Download Free PDF Factoring Trinomials Worksheets and Answer Keys

Do you or your students need some extra practice with factoring trinomials? Our free Factoring Trinomials Worksheet Library shares free PDF worksheets for factoring trinomials when a=1, factoring trinomials when a>1, and factoring by completing the square.

Every factoring trinomials problems worksheet PDF includes an answer key and can be easily saved to your computer and/or printed. You can easily download any factoring trinomials worksheet by clicking on any of the links in the worksheet library below.

And, if you need a quick review of how to factor a trinomial, the second part of this page includes a factoring trinomials review, that includes several sample problems with step-by-step explanations.

All of our factoring trinomials worksheets are a sample activities from the Mashup Math Algebra Worksheet Library available on our website, which includes hundreds of topic-specific algebra practice worksheets.

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Factoring Trinomials Worksheet Library

▶️ Factoring Trinomials (a=1) (A)

▶️ Factoring Trinomials (a=1) (B)

▶️ Extended Practice: Factoring Trinomials (a=1)

▶️ Factoring Trinomials (a>1) (A)

▶️ Factoring Trinomials (a>1) (B)

▶️ Extended Practice: Factoring Trinomials (a>1)

▶️ Factoring/Solving Trinomials by Completing the Square (A)

▶️ Factoring/Solving Trinomials by Completing the Square (B)

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Factoring Trinomials Worksheet Review

If you are struggling to solve problems on any factoring trinomials worksheet, then it will be helpful to review a few step-by-step practice problems to sharpen your skills.

In this section, we will review how to factor trinomials of the form ax²+bx+c for two types of cases:

Factoring Trinomials when the Leading Coefficient a=1
Factoring Trinomials when the Leading Coefficient a>1

Having a strong understanding of how to factor these two types of trinomials will give you a strong foundation that you can build upon as to continue to learn how to factor polynomials.

Factoring Trinomials when the Leading Coefficient a=1

For starters, we can define a trinomial as a 3-term polynomial that can be expressed in the following form:

ax² + bx + c

Whenever the leading coefficient a is equal to 1, we can often use a simple method for finding its factors. A few examples of a trinomial where the leading coefficient a=1 are:

x² + 7x + 12
x² - 9x + 20
x² + 3x - 10

Many trinomials like the ones listed above can be factored by finding two numbers whose sum equals b and whose product equals c.

So, if you can find two numbers that add to b and also multiply to c, then you can find the factors of the trinomial. Now, let’s go ahead and use this method to solve an example problem.

Example: Factor the Trinomial: x² +4x -12

Let’s start by identifying the values of the coefficients a, b, and c as follows:

a = 1
b = 4
c= -12

Notice that, in this example, the leading coefficient, a, is equal to 1.

Now, we can determine the factors of the trinomial x² +4x -12 where a=1, b=4, and c=-12, by finding two numbers that add to b (4) and multiply to c (-12). Using a trial-and-error approach, you can test numbers until you find two numbers that meet this criteria.

In this case, the two numbers that meet this criteria are 6 and -2, because:

6 + (-2) = 4 (and b=4)
6 x (-2) = -12 (and c=-12)

We can now use these two numbers to conclude that the factors of x² +4x -12 are (x+4) and (x-2).

Final Answer: (x + 4)(x - 2)

Figure 01 below shows the step-by-step process for factoring a trinomial when a=1.

Factoring Trinomials when the Leading Coefficient a>1

In some cases, you will have to factor trinomials where the leading coefficient does not equal 1 (i.e. a>1). A few examples of a trinomial where the leading coefficient a>1 include:

2x² + 7x + 13
6x² +11x + 4
5x² + 14x +8

In cases like this, we have to use a completely different strategy than we did for factoring trinomials when a=1.

Example: Factor the Trinomial: 2x² +5x -3

Just like the last example, let’s identify the coefficients a, b, and c:

a = 2
b = 5
c= -3

Notice that, in this example, the leading coefficient, a, is equal to 2, which is greater than 1.

Next, we have to find two numbers that multiply to (a)(c) and also add to b:

(a)(c) = (2)(-3) = -6 → ac = -6
b=5

Now we know that ac=-6 and b=5, so we need to find two numbers that multiply to -6 and add to 5. In this example, the two numbers that meet this criteria are 6 and -1, because:

6 + (-1) = 5 (and b=5)
6 x (-1) = -6 (and ac=-6)

From here, we have to use these two numbers to rewrite the original trinomial 2x² +5x -3 as follows:

2x² +5x -3
2x² +6x -1x -3

Then, we have to group this new polynomial into two binomials as follows:

(2x² +6x) + (-1x -3)

Next, factor out the greatest common factor (GCF) from each group (2x² +6x) and (-1x -3):

2x(x+3) - 1(x+3)

Finally, you can factor out the common binomial as follows:

(2x-1)(x+3)

Final Answer: The factors of 2x² +5x -3 are (2x-1)(x+3)

Figure 02 illustrates the step-by-step process to solving this example where we had to factor a trinomial where a>1.