Classify polynomials by degree

A polynomial’s degree is the greatest exponent of the variable with a nonzero coefficient, determined after like terms are combined; this supports classifying expressions as constant, linear, quadratic, cubic, or other higher-degree polynomials, even when terms are missing or written out of order. The classification distinguishes polynomial structure and supports later work with graphs, functions, factoring, and equations; multivariable degree and the exceptional zero polynomial are not included.

Detailed Explanation: Classify polynomials by degree

The degree of a polynomial is the greatest exponent of the variable that has a nonzero coefficient. After finding the degree, classify the polynomial:

Degree $0$ : constant
Degree $1$ : linear
Degree $2$ : quadratic
Degree $3$ : cubic
Degree $4$ or greater: other higher-degree polynomial

Example

Classify

7x^2-3+4x^3-4x^3+5x-2x^2.

Step 1: Combine like terms.

Group terms with the same power of $x$ :

$(4x^3-4x^3=0)$
$(7x^2-2x^2=5x^2)$
$(5x)$ stays the same
$(-3)$ is the constant term

So the polynomial becomes

5x^2+5x-3.

Step 2: Find the greatest exponent with a nonzero coefficient.

The exponents are $2$ , $1$ , and $0$ . The greatest is $2$ .

Step 3: Classify the polynomial.

A polynomial with degree $2$ is quadratic.

Therefore,

\boxed{\text{The polynomial is quadratic.}}

Remember to combine like terms first, because terms can cancel and change the degree.

Learn by doing: Classify polynomials by degree

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

Practice with unlimited practice problems

Function End Behaviour (Polynomials) - Function to Power and Coefficient

Earned ?