Skill: Classify polynomials by number of terms

To classify a polynomial, first combine like terms. Then count the nonzero terms.

• 1 term: monomial
• 2 terms: binomial
• 3 terms: trinomial
• 4 or more terms: polynomial with that number of terms

Terms are separated by addition or subtraction. A negative term still counts as one term.

Example

Classify:

$$3x^2+4x-2+5x^2-x$$

Step 1: Combine like terms.

Combine the $x^2$ terms:

$$3x^2+5x^2=8x^2$$

Combine the $x$ terms:

$$4x-x=3x$$

The constant $-2$ has no like term, so it stays as it is.

Thus, the expression becomes:

$$8x^2+3x-2$$

Step 2: Count the terms.

The terms are:

$$8x^2,\quad 3x,\quad -2$$

There are $3$ nonzero terms, so the expression is a trinomial.