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Zeros and Multiplicity Practice - Printable Mathematics Worksheets class 10 - Wayground

Zeros and Multiplicity Practice

12 questions

9th - 10th Grade

Mathematics

This Grade 9–10 mathematics worksheet gives students focused practice finding polynomial zeros and identifying each zero’s multiplicity. Through 10 multiple-choice questions, one fill-in-the-blank item, and one open-ended factoring problem, students interpret how a graph crossing or turning at the x-axis relates to odd or even multiplicity, read zeros from factored forms, and match factors with their corresponding zeros. Students also determine real zeros and multiplicities from expressions such as x²(x − 2)³(x − 7), select a polynomial from specified zeros, multiplicities, and degree, identify an excluded zero, and organize factored zeros from least to greatest. The final written-response item asks students to find zeros by factoring and state their multiplicities, providing an opportunity to show complete reasoning. This is a free printable worksheet with a complete answer key for guided practice, independent work, or assessment.

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Zeros and Multiplicity Practice

Total questions: 12

Name
Class
Date
1.

If the graph of a function crosses the x-axis, what does that mean about the multiplicity of that zero?

a)

Even

b)

Odd

c)

None

2.

If the there is a turning point on the x-axis, what does that mean about the multiplicity of that zero?

a)

Even

b)

Odd

c)

None

3.
What are the
zeros of the polynomial
y = 3(x + 4)(x + 1)(x - 3)?
a)
-4, -1, 3
b)
3, -3, 4, 1
c)
4, 1, -3
d)
3, -4, -1, 3
4.
What are the zeros of the polynomial function?
y = x(x - 6)(x + 5)
a)
0, 6, -5
b)
6, -5
c)
0, -6, 5
d)
1, -6, 5
5.
What are the zeros of the function?
a)
4,1
b)
3,1,-2,-5
c)
-3, -1, 2, 5
d)
-2,4
6.
f(x)= x2(x – 2)3(x – 7)

Find and select each real zero and its multiplicity
a)
0 (Mult of 2), 2 (Mult of 3), 7 (mult 1)
b)
2 (Mult of 3), 7 (mult 1)
c)
0, 2, 7
d)
2 (mult of 2), 7 (mult of 3)
7.
f(x)= x2(x – 2)3(x – 7)

Find and select each real zero and its multiplicity
a)
0 (Mult of 2), 2 (Mult of 3), 7 (mult 1)
b)
2 (Mult of 3), 7 (mult 1)
c)
0, 2, 7
d)
2 (mult of 2), 7 (mult of 3)
8.
Select polynomial whose zeros and degree are given.
Zeros: – 5(multiplicity of 3), 9(multiplicity of 2), – 2, 4 with Degree: 7
a)
(x + 5)3(x - 9)2(x + 2)(x - 4)
b)
(x + 5)3(x - 9)2(x + 2)7(x - 4)7
c)
(x + 5)3(x - 9)2(x + 2)
d)
(x + 5)(x - 9)(x + 2)(x - 4)
9.

Which one of these are not a zero of f(x)=−2x(3x+1)2(x+7)7f\left(x\right)=-2x\left(3x+1\right)^2\left(x+7\right)^7  

a)

-2

b)

0

c)

−13-\frac{1}{3}  

d)

-7

10.

What is the multiplicity of the zero x=-5 for the function f(x)=x2(x−1)4(x+5)f\left(x\right)=x^2\left(x-1\right)^4\left(x+5\right) ?

a)

1

b)

2

c)

3

d)

4

11.

Find the zeros of the function by factoring f(x)=x3−5x2+6xf\left(x\right)=x^3-5x^2+6x  . Write your answers from least to greatest, separated by a space.

(a)  

12.

Find the zeros of the function by factoring AND state their multiplicities f(x)=x5+16x4+64x3f\left(x\right)=x^5+16x^4+64x^3  

4 lines
Answer Key

Zeros and Multiplicity Practice

Total questions: 12

1.
b)

Odd

2.
a)

Even

3.
a) -4, -1, 3
4.
a) 0, 6, -5
5.
c) -3, -1, 2, 5
6.
a) 0 (Mult of 2), 2 (Mult of 3), 7 (mult 1)
7.
a) 0 (Mult of 2), 2 (Mult of 3), 7 (mult 1)
8.
a) (x + 5)3(x - 9)2(x + 2)(x - 4)
9.
a)

-2

10.
a)

1

11.
0 2 3
12.
n/a

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FAQs

What does the Zeros and Multiplicity Practice worksheet help students learn?

This worksheet helps Grade 9–10 students find polynomial zeros from factored expressions and determine the multiplicity of each zero. Its 10 multiple-choice items, fill-in-the-blank question, and open-ended factoring problem also connect graph behavior—crossing versus turning at the x-axis—with odd and even multiplicities.

How can I use this worksheet to teach polynomial zeros and multiplicity?

Begin by reviewing how each factor in a factored polynomial identifies a zero and how the factor’s exponent gives its multiplicity. Then use the worksheet’s graph-behavior questions to discuss why a graph crossing the x-axis indicates an odd multiplicity while a turning point on the x-axis indicates an even multiplicity. Finish with the factoring items and ask students to explain how the factors support each answer.

What mistakes should I watch for when students complete this zeros and multiplicity worksheet?

Watch for students reversing the sign of a zero, such as reading x + 4 as 4 instead of −4, or listing the correct zeros without assigning the exponents as multiplicities. Students may also confuse the zeros with the degree when selecting a polynomial, omit a repeated zero, or fail to state multiplicities in the final open-ended factoring response. Check that the fill-in-the-blank answer is written from least to greatest as requested.

How do I assign and grade the Zeros and Multiplicity Practice worksheet?

The worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key for checking the multiple-choice, fill-in-the-blank, and open-ended responses. For printable submissions, teachers can scan student work with the Wayground for Teachers app to support grading. The printable format can also help schools reduce screen time when appropriate.

How can I differentiate this worksheet for students who need a different format?

For the factored polynomial expressions and zeros-and-multiplicity items, open the worksheet’s Advanced Settings to adjust font spacing or choose a larger font size for easier reading. You can also apply a dyslexia-friendly font or translate the worksheet’s directions and questions into another language, depending on your students’ needs.

Where can I find more worksheets like this on Wayground?

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

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