Write a possible polynomial function in factored form with roots 0, -5, 3.

f ( x ) = x ( x + 5 ) ( x − 3 ) f\left(x\right)=x\left(x+5\right)\left(x-3\right) f ( x ) = x ( x + 5 ) ( x − 3 )

f ( x ) = ( x − 5 ) ( x + 3 ) f\left(x\right)=\left(x-5\right)\left(x+3\right) f ( x ) = ( x − 5 ) ( x + 3 )

f ( x ) = x ( x − 5 ) ( x + 3 ) f\left(x\right)=x\left(x-5\right)\left(x+3\right) f ( x ) = x ( x − 5 ) ( x + 3 )

f ( x ) = ( x + 5 ) ( x − 3 ) f\left(x\right)=\left(x+5\right)\left(x-3\right) f ( x ) = ( x + 5 ) ( x − 3 )

Describe the roots of the polynomial function:

A root of -3 with a multiplicity of 1 & a root of 2 with a multiplicity of 2.

A root of 3 with a multiplicity of 1 & a root of -2 with a multiplicity of 2.

A root of 3 with a multiplicity of 2 & a root of -2 with a multiplicity of 1.

A root of -3 with a multiplicity of 2 & a root of 2 with a multiplicity of 1.

Algebra 2 Unit 3 Test Review

Authored by Jill Rodman

Mathematics

8th - 12th Grade

CCSS covered

Used 176+ times

AI Actions

Add similar questions

Adjust reading levels

Convert to real-world scenario

Translate activity

More...

About

This quiz focuses on advanced polynomial operations and analysis, specifically targeting the study of polynomial functions, factoring, roots, and graphical behavior. The content is appropriate for Grade 11 or 12 students studying Algebra 2, as evidenced by the sophisticated concepts including sum and difference of cubes factoring, polynomial long division, application of the Rational Root Theorem, analysis of polynomial zeros and their multiplicities, and interpretation of polynomial graphs. Students need a solid foundation in factoring techniques, understanding of polynomial behavior, facility with synthetic and long division, and the ability to connect algebraic and graphical representations of polynomial functions. The mathematical reasoning required includes recognizing special factoring patterns, applying theoretical concepts like the Fundamental Theorem of Algebra, and analyzing complex relationships between polynomial equations and their graphical representations. Created by Jill Rodman, a Mathematics teacher in the US who teaches grades 8-12. This comprehensive test review quiz provides excellent support for reinforcing key polynomial concepts before summative assessment. The quiz works particularly well as a structured review session, allowing students to practice essential skills systematically before taking their unit test. Teachers can assign this as homework for independent practice, use it during class for collaborative problem-solving, or implement it as a formative assessment tool to identify areas needing additional instruction. The variety of question types—from computational factoring problems to conceptual analysis of roots and graphical interpretation—ensures students engage with polynomials from multiple perspectives. This resource aligns with Common Core standards A-APR.2, A-APR.3, A-APR.6, and F-IF.7, which address polynomial arithmetic, factoring techniques, remainder theorem applications, and analysis of polynomial function graphs.

Content View

Student View

15 questions

Show all answers

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Factor the sum of squares: $x^3+216$

$\left(x-6\right)\left(x^2-6x+36\right)$

$\left(x-6\right)\left(x^2+6x+36\right)$

$\left(x-6\right)\left(x^2+6x+12\right)$

$\left(x+6\right)\left(x^2-6x+36\right)$

Tags

CCSS.HSA.APR.C.4

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Factor the difference of squares: $x^3-216$

$\left(x-6\right)\left(x^2-6x+36\right)$

$\left(x-6\right)\left(x^2+6x+36\right)$

$\left(x-6\right)\left(x^2+6x+12\right)$

$\left(x+6\right)\left(x^2-6x+36\right)$

Tags

CCSS.HSA.APR.C.4

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Divide:

$\left(4x^4+18x^3+3x^2-18x+9\right)\div\left(x+4\right)$

$4x^3+2x^2-5x+2+1$

$4x^3+2x^2-5x+2+\frac{1}{x-4}$

$4x^3+2x^2-5x+\frac{2}{x+4}$

$4x^3+2x^2-5x+2+\frac{1}{x+4}$

Tags

CCSS.HSA.APR.D.6

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Name ALL the possible roots for $f\left(x\right)=2x^3+16x^2+19x+6$

$\pm1,\ \pm2,\ \pm3,\ \pm6$

$\pm1,\ 2,\ 3$

$\pm1,\ \pm2,\ \pm3,\ \pm6,\ \pm\frac{1}{2},\ \pm\frac{3}{2}$

$1,\ 2,\ 3,\ 6,\ \frac{1}{2},\ \frac{3}{2}$

Tags

CCSS.HSA.APR.B.3

MULTIPLE CHOICE QUESTION

1 min • 1 pt

How many roots does the polynomial function have?
$f\left(x\right)=x^4+3x^3+5x^2-3x-6$

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.D.11

MULTIPLE CHOICE QUESTION

1 min • 1 pt

How many zeros does the polynomial equation have?
$0=2x^5+6x^3-32$

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.APR.B.2

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

The function f(x) has a root at -2. Name all roots of this function.
$f\left(x\right)=x^3+9x^2+26x+24$

-2, -3, -4

-2, 3, -4

3, 4

-3, -4

Tags

CCSS.HSF-IF.C.7C

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Find the zeros of the function. (You might want to look at the graph of the function to help you get started!)

$f\left(x\right)=x^3+11x^2+10x-22$

$1,\ -10,\ -2.5$

$1,\ -6+\sqrt{14},\ -6-\sqrt{14}$

$1,\ \sqrt{14}$

$1,\ -12+2\sqrt{14}$

Tags

CCSS.HSF-IF.C.7C

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Factor: $x^4-256$

$\left(x-4\right)\left(x+4\right)\left(x+4\right)\left(x-4\right)$

$\left(x-4\right)\left(x+4\right)\left(x+4i\right)\left(x-4i\right)$

$\left(x-4\right)\left(x+4\right)\left(x^2+16\right)$

$\left(x^2+16\right)\left(x^2-16\right)$

Tags

CCSS.HSA.APR.C.4

10.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Factor: $x^4+8x^2+12=0$

$\left(x-4\right)\left(x+4\right)\left(x+4\right)\left(x-4\right)$

$i\sqrt{2},\ i\sqrt{6}$

$\left(x^2+6\right)\left(x^2-6\right)$

$i\sqrt{2},\ -i\sqrt{2},\ i\sqrt{6},\ -i\sqrt{6}$

Tags

CCSS.HSA-REI.B.4B

Access all questions and much more by creating a free account

Create resources

Host any resource

Get auto-graded reports

Continue with Google

Continue with Email

Continue with Classlink

Continue with Clever

or continue with

Microsoft

Apple

Others

Already have an account?

Similar Resources on Wayground

10 questions

ಬಹುಪದೋಕ್ತಿಗಳು

Quiz

•

10th Grade

15 questions

Polinômios

Quiz

•

8th - 12th Grade

11 questions

Géométrie positionnement

Quiz

•

11th - 12th Grade

10 questions

Find derivative and gradient of a tangent

Quiz

•

12th Grade

20 questions

lecture fonction

Quiz

•

9th - 10th Grade

10 questions

การวัดแนวโน้มเข้าสู่ส่วนกลาง

Quiz

•

10th Grade

20 questions

G12_Math+for+Bus+Eco_Term+Exam_Mock+Test

Quiz

•

12th Grade

20 questions

Circles

Quiz

•

7th - 8th Grade

Popular Resources on Wayground

15 questions

Fractions on a Number Line

Quiz

•

3rd Grade

10 questions

Probability Practice

Quiz

•

4th Grade

15 questions

Probability on Number LIne

Quiz

•

4th Grade

20 questions

Equivalent Fractions

Quiz

•

3rd Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

$fractions$

22 questions

fractions

Quiz

•

3rd Grade

6 questions

Appropriate Chromebook Usage

Lesson

•

7th Grade

10 questions

Greek Bases tele and phon

Quiz

•

6th - 8th Grade

Discover more resources for Mathematics

23 questions

TSI Math Vocabulary

Quiz

•

10th - 12th Grade

15 questions

Graphing Inequalities

Quiz

•

7th - 9th Grade

20 questions

Graphing Inequalities on a Number Line

Quiz

•

6th - 9th Grade

8 questions

8th U5L20 Volume of Sphere

Quiz

•

8th Grade

20 questions

Solving Systems of Equations Review

Quiz

•

8th Grade

20 questions

Slope from a Graph

Quiz

•

8th Grade

15 questions

Combine Like Terms and Distributive Property

Quiz

•

8th - 9th Grade

10 questions

Plotting Points on a Coordinate Plane: Quadrant 1 Essentials

Interactive video

•

6th - 10th Grade

Algebra 2 Unit 3 Test Review

Factor the sum of squares: x3+216x^3+216x3+216

Factor the difference of squares: x3−216x^3-216x3−216

Divide: (4x4+18x3+3x2−18x+9)÷(x+4)\left(4x^4+18x^3+3x^2-18x+9\right)\div\left(x+4\right)(4x4+18x3+3x2−18x+9)÷(x+4)

Name ALL the possible roots for f(x)=2x3+16x2+19x+6f\left(x\right)=2x^3+16x^2+19x+6f(x)=2x3+16x2+19x+6

How many roots does the polynomial function have? f(x)=x4+3x3+5x2−3x−6f\left(x\right)=x^4+3x^3+5x^2-3x-6f(x)=x4+3x3+5x2−3x−6

How many zeros does the polynomial equation have? 0=2x5+6x3−320=2x^5+6x^3-320=2x5+6x3−32

The function f(x) has a root at -2. Name all roots of this function. f(x)=x3+9x2+26x+24f\left(x\right)=x^3+9x^2+26x+24f(x)=x3+9x2+26x+24

Find the zeros of the function. (You might want to look at the graph of the function to help you get started!) f(x)=x3+11x2+10x−22f\left(x\right)=x^3+11x^2+10x-22f(x)=x3+11x2+10x−22

Factor: x4−256x^4-256x4−256

Factor: x4+8x2+12=0x^4+8x^2+12=0x4+8x2+12=0

Access all questions and much more by creating a free account

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Factor the sum of squares: $x^3+216$

Factor the difference of squares: $x^3-216$

Divide:

$\left(4x^4+18x^3+3x^2-18x+9\right)\div\left(x+4\right)$

Name ALL the possible roots for $f\left(x\right)=2x^3+16x^2+19x+6$

How many roots does the polynomial function have?
$f\left(x\right)=x^4+3x^3+5x^2-3x-6$

How many zeros does the polynomial equation have?
$0=2x^5+6x^3-32$

The function f(x) has a root at -2. Name all roots of this function.
$f\left(x\right)=x^3+9x^2+26x+24$

Find the zeros of the function. (You might want to look at the graph of the function to help you get started!)

$f\left(x\right)=x^3+11x^2+10x-22$

Factor: $x^4-256$

Factor: $x^4+8x^2+12=0$