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 177+ times

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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.

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15 questions

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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

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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

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