Algebra 2 Polynomial Operations and Identities Test with Point Values (PDF)

Algebra 2 math test: Polynomial Operations and Identities – Maths PDF

Cover of the book Algebra 2 Math Tests with Answer Keys (PDF)

Download as a PDFThe Algebra 2 tests book with answer keysPrintable PDFSee the book ›

Sommaire

This algebra 2 polynomial operations test for Algebra 2 covers polynomial operations and identities (Common Core A-APR.A.1, A-APR.C.4), with a free PDF to print.

This 45-minute test on polynomial operations and identities 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: Polynomial Operations and Identities
Standards: A-APR.A.1, A-APR.C.4
Time: 45 minutes
Total: 20 points

Algebra 2 polynomial operations test: questions

Question 1 – Add and subtract [2 pts]

Let \(A = 4x^{2} – 3x + 7\) and \(B = x^{2} + 5x – 2\).

\(A + B\) (1 point)
\(A – B\) (1 point)

Question 2 – Multiply [3 pts]

Expand and simplify.

\((x – 3)(x + 8)\) (1 point)
\((2x + 1)(x^{2} – 4x + 3)\) (2 points)

Question 3 – Special products [2 pts]

Use an identity to expand.

\((4x – 1)^{2}\) (1 point)
\((5x + 6)(5x – 6)\) (1 point)

Question 4 – Area model [2 pts]

Rectangle with sides x + 6 and 2x + 1.

A rectangle has side lengths \(x + 6\) and \(2x + 1\). Write its area as a polynomial in standard form.

Question 5 – Mental math [2 pts]

Use an identity (no calculator) to compute \(98^{2}\) and \(61 \cdot 59\).

Question 6 – Pythagorean triple [3 pts]

Triangle for x = 5, y = 2.

Use \(x = 5\) and \(y = 2\) to generate the three sides of a right triangle with the identity \((x^{2} + y^{2})^{2} = (x^{2} – y^{2})^{2} + (2xy)^{2}\). Then verify the triple.

Question 7 – Frame area [2 pts]

Inner rectangle with a border.

A photo \(x\) inches by \(x + 3\) inches has a frame 2 inches wide on every side. Write the area of the frame alone as a polynomial.

Question 8 – Find the error [2 pts]

Aisha wrote \((3x – 2)^{2} = 9x^{2} – 4\). Identify the error and give the correct expansion.

Question 9 – Degree and closure [2 pts]

Find the degree and leading coefficient of \((3x^{2} – 1)(x^{3} + 2x)\). Do not expand fully.

Key facts behind this algebra 2 polynomial operations test

Key facts

Polynomials are closed under addition, subtraction, and multiplication.
Combine like terms; subtract by changing every sign.
Degree of a product = sum of the degrees.
(a ± b)² = a² ± 2ab + b² and (a + b)(a – b) = a² – b².
(x² – y²)² + (2xy)² = (x² + y²)² makes Pythagorean triples.

How to use this algebra 2 polynomial operations 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.

Voter.. post

Free printable PDF