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Factoring Trinomials by Grouping - Printable Math Worksheets class 8 - Wayground

Factoring Trinomials by Grouping

Ryan Ferrill

Created by Ryan Ferrill

18 questions

8th Grade

Math

Updated Sept 2026

Factoring Trinomials by Grouping is a Grade 8 mathematics worksheet that helps students factor quadratic trinomials into equivalent products. Students work with cases where the leading coefficient is 1 or greater than 1, factor out a greatest common factor when needed, identify individual factors, and factor expressions completely. The worksheet also reinforces standard form and the strategies used for different polynomial problem types. A varied question set gives students multiple ways to demonstrate understanding: typed math responses, multiple-choice questions, a drag-and-drop factoring item, a strategy-matching task, and a dropdown question about polynomial notation. These formats move students from producing factored expressions to recognizing correct factors and selecting an appropriate method. This free printable worksheet includes a complete answer key, making it useful for guided practice, independent work, review, or an informal assessment of trinomial factoring skills.

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Factoring Trinomials by Grouping

Total questions: 18

Name
Class
Date
1.

Factor the trinomial to create an equivalent expression:

x2+9x−36x^2+9x-36

(No spaces)

2.

Factor the trinomial to create an equivalent expression:

x2−2x−24x^2-2x-24

(No Spaces)

3.

Factor the trinomial to create an equivalent expression:

3x2−4x−73x^2-4x-7

(No Spaces)

4.

Factor the trinomial to create an equivalent expression:

3x2+4x+13x^2+4x+1

(No Spaces)

5.

Factor the trinomial to create an equivalent expression:

2x2+3x−92x^2+3x-9

(No Spaces)

6.

Factor the trinomial to create an equivalent expression:

2x2−25x+632x^2-25x+63

(No Spaces)

7.

Factor the trinomial to create an equivalent expression:

8x2+9x−148x^2+9x-14

(No Spaces)

8.

Which of the following is ONE of the factors of the trinomial shown below?

3x2+8x−513x^2+8x-51

a)

(3x+17)

b)

(x+3)

c)

(3x+14)

d)

(3x-21)

9.

Factor out GCF first if necessary.

What is the factored form of:

2x2−2x−242x^2-2x-24

Move the correct answer to each box. Not all answers will be used.

​ (a)   (x+​ (b)   )(x-​ (c)   )

Choose from the below words
2
3
4
1
6
5
10.

What is the factored form of:

4x2+18x+84x^2+18x+8

a)

2(x+4)(2x+1)

b)

4(x+2)(x+4)

c)

2(x+1)(2x+4)

d)

(2x+4)(2x+1)

11.

Match each problem type to the strategy used to solve.

Factoring Trinomials

a>1

Diamond with grouping

Factoring Trinomials

a=1

Diamond only

Multiplying Polynomials

Box & FOIL

Adding Polynomials

Combining Like Terms

Subtracting Polynomials

KCC and then combine

12.

A trinomial written in ​ (a)   form lists the terms in ​ (b)   order based on the variable term ​ (c)   . For example: x2+8x+12x^2+8x+12

Choose from the below words
standard
descending
exponents
ascending
coefficients
superior
13.
Question Image

a)

(x - 12)(x - 3)

b)

(x + 3)(x + 12)

c)

(x + 12)(x - 3)

d)

(x + 3)(x - 12)

14.
Factor completely.
3x2 + 10x - 8
a)
(3x + 2)(x + 4)
b)
(7x + 5)(x + 2)
c)
(3x - 2)(x + 4)
d)
(7x - 3)(x - 4)
15.
Factor completely.
5x2 - 7x + 2
a)
5(x - 2)(x + 1)
b)
(5x - 2)(x + 1)
c)
(7x - 1)(x - 4)
d)
(5x - 2)(x - 1)
16.

What is the value of y for the solution to the system?

x – 2y = 9

x + 3y = –1

a)

-2

b)

2

c)

3

d)

-3

17.
Which linear inequality represents the graph?

Which linear inequality represents the graph?

a)

y<−2x−4y<-2x-4  

b)

y≤−2x−4y\le-2x-4

c)

y>−2x−4y>-2x-4

d)

y<−4x−2y<-4x-2

18.
Select the graph for 5x+ y ≤ -1 .
Select the graph for 5x+ y ≤  -1 .
a)
A
b)
B
c)
C
d)
D
WaygroundAnswer Key

Factoring Trinomials by Grouping

Total questions: 18

1.

(x+12)(x−3)\left(x+12\right)\left(x-3\right)

2.

(x+4)(x−6)\left(x+4\right)\left(x-6\right)

3.

(3x−7)(x+1)\left(3x-7\right)\left(x+1\right)

4.

(3x+1)(x+1)\left(3x+1\right)\left(x+1\right)

5.

(x+3)(2x−3)\left(x+3\right)\left(2x-3\right)

6.

(x−9)(2x−7)\left(x-9\right)\left(2x-7\right)

7.

(x+2)(8x−7)\left(x+2\right)\left(8x-7\right)

8.
a)

(3x+17)

9.
2, 3, 4
10.
a)

2(x+4)(2x+1)

11.

Factoring Trinomials

a>1

 - 

Diamond with grouping

, 

Factoring Trinomials

a=1

 - 

Diamond only

, 

Multiplying Polynomials

 - 

Box & FOIL

, 

Adding Polynomials

 - 

Combining Like Terms

, 

Subtracting Polynomials

 - 

KCC and then combine

12.
standard, descending, exponents
13.
b)

(x + 3)(x + 12)

14.
c) (3x - 2)(x + 4)
15.
d) (5x - 2)(x - 1)
16.
a)

-2

17.
a)

y<−2x−4y<-2x-4  

18.
d) D

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FAQs

What does this factoring trinomials worksheet help Grade 8 students learn?

This Grade 8 mathematics worksheet focuses on factoring quadratic trinomials by grouping, including expressions with a leading coefficient of 1 or greater than 1. Students produce equivalent factored expressions, factor out a GCF when necessary, identify individual factors, and recognize completely factored forms through typed responses, selected-response items, drag-and-drop, matching, and dropdown questions.

How can I use this worksheet to teach factoring trinomials by grouping?

Introduce the worksheet by modeling how to check the product and sum of the factors, then show how the process changes when the leading coefficient is greater than 1. Use the typed factoring items for guided practice, pause at the drag-and-drop question to discuss factoring out the GCF first, and use the matching item to connect each trinomial type with its strategy. Finish by asking students to explain how multiplying their factors verifies the original trinomial.

What mistakes should I watch for when students complete this factoring worksheet?

Watch for students who skip factoring out the GCF, choose factors with the wrong signs, or stop before the expression is completely factored. Students may also confuse the strategies for trinomials with a leading coefficient of 1 and those with a coefficient greater than 1, or enter a mathematically correct response in the wrong typed format when no spaces are requested. The multiple-choice and drag-and-drop items can reveal whether an error comes from identifying factors or arranging the final product.

How do I assign and grade this factoring trinomials worksheet?

On Wayground, assign Factoring Trinomials by Grouping as a printable PDF or as a digital quiz. The worksheet includes a complete answer key for checking typed responses, selected answers, matching, drag-and-drop, and dropdown items. Printable submissions can also be graded by scanning student work with the Wayground for Teachers app.

How can I differentiate this factoring trinomials worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing and font size so the algebraic expressions and answer choices are easier to read. You can also enable a dyslexia-friendly font or translate the worksheet when students need language or reading support. These adjustments apply to the factoring problems and their varied response formats, including the matching and drag-and-drop items.

Where can I find more free worksheets like this on Wayground?

Wayground offers a broad collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to support mastery of essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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