Polynomials Worksheet with Answers – Algebra 1 (Free PDF)

Problem 1 Standard Form and Degree ★★★

Write 7x − 4x³ + 2 in standard form. State its degree and leading coefficient.

Problem 2 Name Each Polynomial ★★★

Classify each polynomial by number of terms and state its degree.

1. 9x⁴
2. x² − 6
3. 2x³ + x − 8

Problem 3 Evaluate a Polynomial ★★★

Evaluate P(x) = x² − 3x + 5 at x = −2.

Problem 4 Add Two Trinomials ★★★

Simplify (4x² + 3x − 1) + (x² − 6x + 9).

Problem 5 Subtract Two Trinomials ★★★

Simplify (7x² − 2x + 6) − (3x² + 5x − 1).

Problem 6 Multiply Monomials ★★★

Multiply.

1. (3x²)(−5x⁴)
2. (6a³b)(−2ab⁴)

Problem 7 Distribute a Monomial ★★★

Multiply 4x(2x² − 3x + 7).

Problem 8 Multiply Two Binomials ★★★

Multiply (x + 8)(x − 3).

Problem 9 Binomials with Coefficients ★★★

Multiply (6x − 7)(4x + 9).

Problem 10 Trinomial Times Binomial ★★★

Multiply (x² − 4x + 6)(x + 3). Use the box to organize the products.

Problem 11 Square a Binomial ★★★

Expand.

1. (x + 7)² (the square shows the area)
2. (3x − 2)²

Problem 12 Difference of Squares ★★★

Multiply (9k + 11)(9k − 11).

Problem 13 Three Polynomials at Once ★★★

Simplify (5x² − 3x + 8) − (2x² + x − 6) + (x² − 4).

Problem 14 Closure Check ★★★

Multiply (2x + 1)(x² − 3). Is the product a polynomial? State its degree and explain how degrees relate here.

Problem 15 Patio with a Pond ★★★

A rectangular patio is x + 9 feet long and x + 4 feet wide. A square pond with side x feet sits in one corner. Write the area of the patio not covered by the pond as a polynomial in simplest form.

Problem 16 Ticket Revenue ★★★

A theater sells (30 + 5x) tickets at a price of (40 − 2x) dollars, where x is the number of $1 price changes. Write the revenue as a polynomial in standard form, then evaluate it for x = 3.

Problem 17 Profit from Revenue and Cost ★★★

A club sells x bracelets. Revenue is R(x) = −3x² + 90x dollars and cost is C(x) = 12x + 250 dollars. Write the profit polynomial P(x) = R(x) − C(x) and find the profit for x = 10.

Problem 18 Cube of a Binomial ★★★

Expand (x + 2)³ by writing it as (x + 2)(x + 2)² and multiplying.

Problem 19 Arithmetic with Special Products ★★★

Use a special product, not a calculator, to find 47 × 53 and 62².

Problem 20 Find the Error ★★★

A student wrote (x − 4)² = x² − 16 and (x + 3)(x − 3) = x² − 6x − 9. Decide which statements are wrong, explain each error and give the correct expansions.