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Algebra 2 Final Exam - Printable Mathematics Worksheets - Wayground

Algebra 2 Final Exam

12 questions

10th - 10th Grade

Mathematics

The Algebra 2 Final Exam is a free printable Grade 10 mathematics worksheet that reviews three core polynomial skills: performing polynomial long division, factoring polynomials, and identifying polynomial end behavior. Its 12 multiple-choice questions are distributed across these skills, giving students a focused review of algebraic procedures and graphical reasoning. Students must select the correct result for each polynomial task, making the worksheet useful for final review, independent practice, or a short summative check. The long-division items reinforce accurate computation, the factoring items assess recognition of equivalent factored forms, and the end-behavior items connect polynomial structure to how a graph behaves on either end. A complete answer key is included, and the worksheet is available as a free printable PDF for classroom or take-home use.

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Worksheets

Algebra 2 Final Exam

Total questions: 12

Name
Class
Date
1.

Perform the polynomial long division: x3−6x2+11x−6x−2\frac{x^3 - 6x^2 + 11x - 6}{x - 2} .

a)

x2−4x+3x^2 - 4x + 3

b)

x2−4x+5x^2 - 4x + 5

c)

x2−3x+2x^2 - 3x + 2

d)

x2−3x+1x^2 - 3x + 1

2.

Factor the polynomial: x2−5x+6x^2 - 5x + 6 .

a)

(x−2)(x−3)(x - 2)(x - 3)

b)

(x+2)(x−3)(x + 2)(x - 3)

c)

(x−1)(x−6)(x - 1)(x - 6)

d)

(x+1)(x−6)(x + 1)(x - 6)

3.

Identify the end behavior of the polynomial f(x)=−2x4+3x3−x+5f(x) = -2x^4 + 3x^3 - x + 5 .

a)

x→∞ y→∞x\rightarrow\infty\ y\rightarrow\infty x→−∞y→−∞x\rightarrow-\infty y\rightarrow-\infty

b)

x→∞ y→−∞x\rightarrow\infty\ y\rightarrow-\infty x→−∞ y→∞x\rightarrow-\infty\ y\rightarrow\infty

c)

x→∞ y→−∞x\rightarrow\infty\ y\rightarrow-\infty x→−∞ y→−∞x\rightarrow-\infty\ y\rightarrow-\infty

d)

x→∞ y→∞x\rightarrow\infty\ y\rightarrow\infty x→−∞ y→∞x\rightarrow-\infty\ y\rightarrow\infty

4.

Perform the polynomial long division: 2x3+3x2−5x+6x+1\frac{2x^3 + 3x^2 - 5x + 6}{x + 1} .

a)

2x2+x−6 +12x+12x^2+x-6\ +\frac{12}{x+1}

b)

2x2+x−72x^2 + x - 7

c)

2x2+x−52x^2 + x - 5

d)

2x2+x−42x^2 + x - 4

5.

Factor the polynomial: x2+7x+12x^2 + 7x + 12 .

a)

(x+3)(x+4)(x + 3)(x + 4)

b)

(x+2)(x+6)(x + 2)(x + 6)

c)

(x+1)(x+12)(x + 1)(x + 12)

d)

(x+4)(x+5)(x + 4)(x + 5)

6.

Perform the polynomial long division: x3+2x2−x−2x−1\frac{x^3 + 2x^2 - x - 2}{x - 1} .

a)

x2+3x+2x^2 + 3x + 2

b)

x2+x+1x^2 + x + 1

c)

x2+x+2x^2 + x + 2

d)

x2+3x+1x^2 + 3x + 1

7.

Factor the polynomial: x2−9x^2 - 9 .

a)

(x−3)(x+3)(x - 3)(x + 3)

b)

(x−3)(x−3)(x - 3)(x - 3)

c)

(x+3)(x+3)(x + 3)(x + 3)

d)

(x−9)(x+1)(x - 9)(x + 1)

8.

Identify the end behavior of the polynomial f(x)=−x6+4x4−x2+2f(x) = -x^6 + 4x^4 - x^2 + 2 .

a)

x→∞ y→−∞x\rightarrow\infty\ y\rightarrow-\infty x→−∞ y→−∞x\rightarrow-\infty\ y\rightarrow-\infty

b)

x→∞ y→∞x\rightarrow\infty\ y\rightarrow\infty x→−∞ y→∞x\rightarrow-\infty\ y\rightarrow\infty

9.

Perform the polynomial long division: 3x3−x2+4x−2x−1\frac{3x^3 - x^2 + 4x - 2}{x - 1} .

a)

3x2+2x+6 +4x−13x^2+2x+6\ +\frac{4}{x-1}

b)

3x2+2x+23x^2 + 2x + 2

c)

3x2+2x+43x^2 + 2x + 4

d)

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

10.

Identify the end behavior of the polynomial f(x)=5x3−2x2+x−1f(x) = 5x^3 - 2x^2 + x - 1 .

a)

x→∞ y→∞x\rightarrow\infty\ y\rightarrow\infty x→−∞ y→−∞x\rightarrow-\infty\ y\rightarrow-\infty

b)

x→∞ y→−∞x\rightarrow\infty\ y\rightarrow-\infty x→−∞ y→∞x\rightarrow-\infty\ y\rightarrow\infty

11.

Factor the polynomial: x2+2x−8x^2 + 2x - 8 .

a)

(x+4)(x−2)(x + 4)(x - 2)

b)

(x+2)(x−4)(x + 2)(x - 4)

c)

(x+1)(x−8)(x + 1)(x - 8)

d)

(x+8)(x−1)(x + 8)(x - 1)

12.

Identify the end behavior of the polynomial f(x)=−4x5+3x3−x+7f(x) = -4x^5 + 3x^3 - x + 7 .

a)

x→∞ y→−∞x\rightarrow\infty\ y\rightarrow-\infty x→−∞ y→∞x\rightarrow-\infty\ y\rightarrow\infty

b)

x→∞ y→∞x\rightarrow\infty\ y\rightarrow\infty x→−∞ y→−∞x\rightarrow-\infty\ y\rightarrow-\infty

Answer Key

Algebra 2 Final Exam

Total questions: 12

1.
a)

x2−4x+3x^2 - 4x + 3

2.
a)

(x−2)(x−3)(x - 2)(x - 3)

3.
c)

x→∞ y→−∞x\rightarrow\infty\ y\rightarrow-\infty x→−∞ y→−∞x\rightarrow-\infty\ y\rightarrow-\infty

4.
a)

2x2+x−6 +12x+12x^2+x-6\ +\frac{12}{x+1}

5.
a)

(x+3)(x+4)(x + 3)(x + 4)

6.
a)

x2+3x+2x^2 + 3x + 2

7.
a)

(x−3)(x+3)(x - 3)(x + 3)

8.
a)

x→∞ y→−∞x\rightarrow\infty\ y\rightarrow-\infty x→−∞ y→−∞x\rightarrow-\infty\ y\rightarrow-\infty

9.
a)

3x2+2x+6 +4x−13x^2+2x+6\ +\frac{4}{x-1}

10.
a)

x→∞ y→∞x\rightarrow\infty\ y\rightarrow\infty x→−∞ y→−∞x\rightarrow-\infty\ y\rightarrow-\infty

11.
a)

(x+4)(x−2)(x + 4)(x - 2)

12.
a)

x→∞ y→−∞x\rightarrow\infty\ y\rightarrow-\infty x→−∞ y→∞x\rightarrow-\infty\ y\rightarrow\infty

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FAQs

What does the Algebra 2 Final Exam worksheet cover?

This Grade 10 worksheet contains 12 multiple-choice questions on three specific polynomial skills: performing polynomial long division, factoring polynomials, and identifying end behavior. Completing the items requires students to carry out algebraic procedures, recognize correct factored forms, and use polynomial characteristics to determine how a graph behaves at its ends.

How can I use this worksheet to teach polynomial long division, factoring, and end behavior?

Use the worksheet after modeling one example of each task type, then have students explain why each selected multiple-choice answer is correct. Ask students to compare the long-division quotient with the original polynomial, verify a factored expression by multiplication, and justify an end-behavior choice using the polynomial's degree and leading term. Reviewing the three item types in this sequence helps connect calculation, equivalent expressions, and graph interpretation.

What mistakes should I watch for on this polynomial worksheet?

Students may lose signs or misalign terms during polynomial long division, especially when subtracting intermediate products. In the factoring questions, watch for factors that do not multiply back to the original polynomial or that omit a common factor. For end-behavior items, students may focus on the constant term instead of the degree and leading coefficient, which determine the graph's behavior at the ends.

How do I assign and grade the Algebra 2 Final Exam worksheet?

The worksheet is available as a printable PDF and as a digital quiz on Wayground, with a complete answer key for all 12 multiple-choice questions. You can assign the digital version for online completion or print it for written work, then grade printable submissions by scanning student work with the Wayground for Teachers app.

How can I differentiate this polynomial worksheet for my students?

For this 12-question multiple-choice worksheet, use Advanced Settings to adjust font spacing and font size so polynomial expressions and answer choices are easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language when those changes support access to the long-division, factoring, and end-behavior items.

Where can I find more 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 essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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