Algebra 2 Dividing Polynomials and the Remainder Theorem Test with Point Values (PDF)

Algebra 2 math test: Dividing Polynomials and the Remainder Theorem – Maths PDF

Sommaire

This algebra 2 polynomial division test for Algebra 2 covers dividing polynomials and the remainder theorem (Common Core A-APR.B.2, A-APR.D.6), with a free PDF to print.

This 45-minute test on polynomial division and the Remainder Theorem has 9 questions worth 20 points in total. The questions move from direct skills to multi-step problems. Show your work, because partial credit is given for a correct setup and sound reasoning.

Time and points

About this test

Grade: Algebra 2
Chapter: Dividing Polynomials and the Remainder Theorem
Standards: A-APR.B.2, A-APR.D.6
Time: 45 minutes
Total: 20 points

Algebra 2 polynomial division test: questions

Question 1 – Long division [3 pts]

Divide \(2x^{3} + 5x^{2} – 14x + 8\) by \(2x – 1\) using long division.

Question 2 – Synthetic division [3 pts]

Use synthetic division to divide \(3x^{3} – 5x^{2} + 4\) by \(x – 2\). Write the result as a quotient plus a remainder term.

Question 3 – Remainder Theorem [2 pts]

Find the remainder when \(x^{3} + 2x^{2} – 9x – 18\) is divided by \(x + 3\). Is \(x + 3\) a factor?

Question 4 – Graph and factors [2 pts]

Graph of p(x) with x-intercepts at -1, 2, 3.

The graph of a cubic polynomial \(p(x)\) with leading coefficient 1 crosses the x-axis at \(-1\), \(2\), and \(3\). Write \(p(x)\) in factored form and find \(p(0)\).

Question 5 – Find the unknown [2 pts]

The polynomial \(x^{3} – 3x^{2} + kx + 10\) has a factor \(x – 5\). Find \(k\).

Question 6 – Quotient form [2 pts]

Write \(\frac{x^{2} + 4x + 7}{x + 1}\) in the form \(q(x) + \frac{r}{x + 1}\).

Question 7 – Storage bin [2 pts]

Storage bin with unknown width.

A storage bin has volume \(x^{3} + 8x^{2} + 17x + 10\text{ in}^{3}\), length \(x + 5\), and height \(x + 1\). Find the width.

Question 8 – Find the error [2 pts]

Jamal’s work for x³ + 2x – 3 divided by x – 1.

Jamal divided \(x^{3} + 2x – 3\) by \(x – 1\) with the grid shown, using coefficients 1, 2, -3. Explain his error and find the correct quotient and remainder.

Question 9 – Factor completely [2 pts]

Given that \(x + 1\) is a factor of \(x^{3} + 6x^{2} + 11x + 6\), factor the polynomial completely.

Key facts behind this algebra 2 polynomial division test

Key facts

a(x) / b(x) = q(x) + r(x) / b(x) with deg r < deg b.
Synthetic division works for divisors x – k.
Remainder Theorem: p(x) ÷ (x – k) has remainder p(k).
Factor Theorem: x – k is a factor if and only if p(k) = 0.
Include 0 coefficients for missing powers.

How to use this algebra 2 polynomial division test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Algebra 2 chapters: Algebra 2 math.

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