Polynomials and Degree
A polynomial is a sum of terms with whole-number exponents.
About this topic
A polynomial is a sum of terms, each a number times a variable raised to a non-negative whole-number power, like 4x³ − 2x + 7. Names depend on the number of terms: monomial, binomial, trinomial. The degree is the highest exponent, and the leading coefficient is attached to that term.
Writing a polynomial in standard form means listing terms from highest power to lowest. In 4x³ − 2x + 7 the degree is 3 and the leading coefficient is 4. The degree names the type: degree 1 is linear, 2 is quadratic, 3 is cubic, 4 is quartic. The degree also tells you the most roots the polynomial can have and gives a clue about the shape of its graph.
Polynomials are everywhere. Formulas for area (length times width), volume, projectile height, and cost models are all polynomials, and engineers use them to approximate more complicated curves because they are easy to compute. Computer graphics draw smooth curves with cubic polynomials.
Expressions like 1/x or √x or 2ˣ are not polynomials because the variable is in a denominator, under a root or in an exponent. For multi-variable terms, add the exponents to find the degree of that term, so 3x²y has degree 3.
Key ideas
- Monomial, binomial, trinomial
- Degree is the highest exponent
- Write in standard form from high to low
Quick check
Use cases: where Polynomials and Degree helps
- Homework: review the key idea behind Polynomials and Degree before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Polynomials and Degree without notes.
- Visual learning: play with the interactive lab to see how Polynomials and Degree changes when you adjust its inputs.
- Teaching a friend: explain Polynomials and Degree in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Polynomials and Degree?
A polynomial is a sum of terms with whole-number exponents.
What will I learn in Polynomials and Degree?
Monomial, binomial, trinomial. Degree is the highest exponent. Write in standard form from high to low.
Is Polynomials and Degree part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Polynomials and Degree lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Polynomials and Degree?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
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