Polynomial — Definition and Degree
A polynomial is an algebraic expression made using variables, constants, coefficients, and non-negative whole number powers of variables. The degree is the highest power of the variable present in the polynomial.
Practice This ConceptMain explanation
Teacher explanation
In one variable, expressions like 3x + 2, x² - 5x + 6, and 7 are polynomials because the powers of x are whole numbers. Expressions with variables in the denominator or square root of the variable are not polynomials at this level. The degree tells the type of polynomial, such as linear for degree 1 and quadratic for degree 2.
Example
In 5x³ - 2x + 8, the highest power of x is 3, so the degree is 3. In 4x + 9, the degree is 1, so it is linear.
Simple analogy
Degree means highest power, not biggest number.
Common confusion
Students sometimes count the number of terms as the degree. For example, 2x + 7 has two terms, but its degree is 1, not 2.
Exam tip
First arrange mentally by powers of the variable, then identify the highest exponent. Do not use the coefficient to decide the degree.
Study the polynomial — definition and degree diagram carefully
Use the labelled diagram to keep polynomial — definition and degree clear in short answers and revision.
What this diagram makes clear
This diagram keeps the labels and direction of polynomial — definition and degree in the right order.
Where this helps in exams
Use this for labelled diagram work and short exam answers on polynomial — definition and degree.
Revision cue
Revise polynomial — definition and degree through the labels before writing the answer.
Answer writing and exam use
1-mark use
Write the exact meaning of polynomial — definition and degree in one clean line.
2-mark use
Define polynomial — definition and degree and add one example or condition.
3-mark use
Explain polynomial — definition and degree, show the method or example, and mention the common mistake.
Practice this concept with focused MCQs
Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.
Help improve this page
Found something confusing, incorrect, or missing?