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Factoring Polynomials - Printable Mathematics Worksheets - Wayground

Factoring Polynomials

20 questions

9th - 12th Grade

Mathematics

Factoring Polynomials is a mathematics worksheet for students in Grades 9–12 who are developing fluency with rewriting polynomials as products of factors. Across 20 questions, students respond to factoring prompts through four multiple-choice items, 15 math-response items, and one drag-and-drop item that requires the factors to be placed in order with the largest number first. The varied formats let teachers check both recognition and independent factoring. Students select or enter factorized expressions, show their work on several response items, and organize factors in the drag-and-drop task. This free printable worksheet includes a complete answer key, making it useful for guided practice, independent work, homework, or a skills check in an algebra unit.

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Worksheets

Factoring Polynomials

Total questions: 20

Name
Class
Date
1.

Factor: 5x+105x+10

a)

5(x+10)(x−10)5\left(x+10\right)\left(x-10\right)

b)

5(x+10)5\left(x+10\right)

c)

5(x+2)5\left(x+2\right)

d)

5(x+2)(x−2)5\left(x+2\right)\left(x-2\right)

2.

Factor: x2−8xx^2-8x

3.

Factor: 2x2+6x2x^2+6x

4.

Factor: 3x2y−12xy33x^2y-12xy^3

a)

3(x2y−4xy3)3\left(x^2y-4xy^3\right)

b)

3xy(xy−4y3)3xy\left(xy-4y^3\right)

c)

3x2y(1−4xy3)3x^2y\left(1-4xy^3\right)

d)

3xy(x−4y2)3xy\left(x-4y^2\right)

5.

Factor: x2+7x+12x^2+7x+12 =(​​ (a)   )(​ (b)   )

*Write with the largest number first.

Choose from the below words
x+4
x+3
x+12
x-3
x-4
6.

Factor: x2−9x+20x^2-9x+20

a)

(x−5)(x−4)\left(x-5\right)\left(x-4\right)

b)

(x−5)(x+4)\left(x-5\right)\left(x+4\right)

c)

(x+10)(x+2)\left(x+10\right)\left(x+2\right)

d)

(x−10)(x−2)\left(x-10\right)\left(x-2\right)

7.

Factor: x2+12x+32x^2+12x+32

8.

Factor: x2−15x+50x^2-15x+50

9.

Factor: 2x2+13x+152x^2+13x+15

*Upload your work*

10.

Factor: 3x2−13x+43x^2-13x+4

*Upload your work*

11.

Factor: 5x2−33x−145x^2-33x-14

*Upload your work*

12.

Factor: 6x2+19x+86x^2+19x+8

*Upload your work*

13.

Factor: x2−9x^2-9

a)

(x−9)2\left(x-9\right)^2

b)

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

c)

(x−3)2\left(x-3\right)^2

d)

(x+9)(x−9)\left(x+9\right)\left(x-9\right)

14.

Factor: x2−64x^2-64

15.

Factor: x2−36x^2-36

16.

Factor: 2x2−2002x^2-200

*Upload your work*

17.

Factor by Grouping: x3+3x2+2x+6x^3+3x^2+2x+6

*Upload your work*

18.

Factor by Grouping: x3+5x2−2x−10x^3+5x^2-2x-10

*Upload your work*

19.

Factor by Grouping: x3+3x2+4x+12x^3+3x^2+4x+12

*Upload your work*

20.

Factor by Grouping: 2x3+14x2+5x+352x^3+14x^2+5x+35

*Upload your work*

Answer Key

Factoring Polynomials

Total questions: 20

1.
c)

5(x+2)5\left(x+2\right)

2.

x(x−8)x\left(x-8\right)

3.

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

4.
d)

3xy(x−4y2)3xy\left(x-4y^2\right)

5.
x+4, x+3
6.
a)

(x−5)(x−4)\left(x-5\right)\left(x-4\right)

7.

(x+8)(x+4)\left(x+8\right)\left(x+4\right)

8.

(x−5)(x−10)\left(x-5\right)\left(x-10\right)

9.

(x+5)(2x+3)\left(x+5\right)\left(2x+3\right)

10.

(x−4)(3x−1)\left(x-4\right)\left(3x-1\right)

11.

(x−7)(5x+2)\left(x-7\right)\left(5x+2\right)

12.

(3x+8)(2x+1)\left(3x+8\right)\left(2x+1\right)

13.
b)

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

14.

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

15.

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

16.

2(x+10)(x−10)2\left(x+10\right)\left(x-10\right)

17.

(x2+2)(x+3)\left(x^2+2\right)\left(x+3\right)

18.

(x2−2)(x+5)\left(x^2-2\right)\left(x+5\right)

19.

(x2+4)(x+3)\left(x^2+4\right)\left(x+3\right)

20.

(2x2+5)(x+7)\left(2x^2+5\right)\left(x+7\right)

FAQs

What does this factoring polynomials worksheet help students practice?

This Grade 9–12 mathematics worksheet helps students rewrite polynomials as products of factors. Its 20 items combine multiple-choice recognition, typed math responses, uploaded work, and a drag-and-drop task requiring factors to be ordered with the largest number first, so students practice both identifying and producing factored forms.

How can I use this worksheet to teach students to factor polynomials?

Begin by modeling how a polynomial can be rewritten as a product of factors, then have students explain how they know a proposed factored form matches the original expression. Use the multiple-choice items for guided discussion, move to the independent math-response questions, and finish by reviewing the drag-and-drop ordering direction and the uploaded-work responses.

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

Watch for students who stop at an unfactored expression, confuse factoring with expanding, or enter a factorized form without checking that it represents the original polynomial. In the drag-and-drop item, students may also choose the right factors but place the larger number second; the upload-work items can reveal skipped or unclear steps behind an answer.

How do I assign and grade this factoring polynomials worksheet?

Wayground provides this worksheet as a printable PDF and as a digital quiz, and it includes a complete answer key for checking all 20 items. Printable submissions can be graded by scanning student work with the Wayground for Teachers app, while the digital version can be assigned through Wayground for online responses.

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

Use the worksheet’s Advanced Settings to adjust font spacing or font size so the polynomial expressions and response areas are easier to read and use. You can also enable a dyslexia-friendly font or translate the factoring prompts into another language when that supports access to the worksheet format.

Where can I find more worksheets like this on Wayground?

Wayground offers a broad collection of free printable worksheets and practice problems across all 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.