Practice Polynomials in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Worksheet PDF Free Answer-key PDF Family

Quick Recap

An expression built by adding terms that consist of constants multiplied by variables raised to non-negative integer powers.

A sum of terms like 3x2+2x−53x^2 + 2x - 5. The highest power is the degree.

Showing a random 20 of 50 problems.

Example 1

easy
Classify 5x4−x+25x^4 - x + 2 by degree and number of terms.

Example 2

easy
Classify 4x−54x - 5 by degree and number of terms.

Example 3

medium
Is x+1\sqrt{x} + 1 a polynomial? Why?

Example 4

medium
Subtract (2x3−x+4)(2x^3 - x + 4) from (5x3+3x2−2)(5x^3 + 3x^2 - 2).

Example 5

medium
Find a polynomial that represents the area of a rectangle with length x+4x + 4 and width x−2x - 2.

Example 6

medium
Expand (x−4)2(x - 4)^2.

Example 7

medium
Multiply: 3x(2x2−x+4)3x(2x^2 - x + 4).

Example 8

easy
Is x−2+3x^{-2} + 3 a polynomial?

Example 9

easy
Add: (2x+3)+(x−5)(2x + 3) + (x - 5).

Example 10

hard
Expand (x+2)3(x + 2)^3.

Example 11

medium
Evaluate the polynomial x2−2x+1x^2 - 2x + 1 at x=1x = 1.

Example 12

hard
Divide x3+2x2−5x−6x^3 + 2x^2 - 5x - 6 by x−2x - 2 using synthetic division.

Example 13

easy
What is the degree of 3x4−2x+13x^4 - 2x + 1?

Example 14

medium
Find the degree and leading coefficient of (2x2−1)(x3+4)(2x^2 - 1)(x^3 + 4) after expansion.

Example 15

medium
Multiply: (x+2)(x+3)(x + 2)(x + 3).

Example 16

easy
What is the leading coefficient of −4x3+9x−1-4x^3 + 9x - 1?

Example 17

hard
What is the sum of all coefficients of (3x−2)5(3x - 2)^5 when expanded?

Example 18

easy
Evaluate P(x)=x3−2x+1P(x) = x^3 - 2x + 1 at x=2x = 2.

Example 19

medium
Expand (2x−1)2(2x - 1)^2.

Example 20

medium
What is the degree of (x2+1)(x3−x)(x^2 + 1)(x^3 - x)?
← Back to Polynomials Worked Examples Formula Explained