Polynomials Test – Algebra 1 Math (Printable PDF)

Question 1 Standard Form (2 points)

Write 5x − 2x³ + 9x² − 4 in standard form. State its degree and its leading coefficient.

Question 2 Add Polynomials (2 points)

Simplify (6x² − 4x + 7) + (−2x² + 9x − 3).

Question 3 Subtract Polynomials (2 points)

Simplify (8x² + 3x − 5) − (5x² − 6x + 2).

Question 4 Area of a Rectangle (2 points)

A banner for the robotics fair is a rectangle 7x + 2 inches long and 4x − 5 inches wide. Express its area in square inches as a polynomial in standard form.

Question 5 Trinomial Times Binomial (3 points)

Multiply (x − 3)(x² + 5x − 2) and write the answer in standard form.

Question 6 Special Products (2 points)

Expand.

1. (4x − 3)² (1 point)
2. (2x + 7)(2x − 7) (1 point)

Question 7 Grass Around the Pool (3 points)

A yard is 2x + 7 feet long and x + 4 feet wide. A square pool with side x + 1 feet sits in one corner, and the rest of the yard is grass.

1. Write the grass area as a polynomial in simplest form. (2 points)
2. Find the grass area when x = 5. (1 point)

Question 8 Mental Math with Algebra (2 points)

Use a special product to find each value without a calculator, and show the structure.

1. 38 × 42 (1 point)
2. 71² (1 point)

Question 9 Explain the Error (2 points)

Dev claims that (x + 5)² = x² + 25. Explain his error and write the correct expansion.