Polynomials Examples in Math
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Polynomials.
This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.
Concept 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 3x^2 + 2x - 5. The highest power is the degree.
Read the full concept explanation →How to Use These Examples
- Read the first worked example with the solution open so the structure is clear.
- Try the practice problems before revealing each solution.
- Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea: Polynomials are building blocks—simple yet surprisingly powerful.
Common stuck point: Degree determines the basic shape and maximum number of roots.
Sense of Study hint: Circle the term with the highest exponent first, then arrange all terms from highest to lowest power.
Worked Examples
Example 1
easySolution
- 1 Identify the exponent of each term: x^3 has degree 3, x^2 has degree 2, x has degree 1, -7 has degree 0.
- 2 The degree of the polynomial is the highest exponent.
- 3 The degree is 3.
Answer
Example 2
mediumExample 3
mediumPractice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easyExample 2
mediumRelated Concepts
Background Knowledge
These ideas may be useful before you work through the harder examples.