Skill: 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.