Classify
Use degree and number of terms
The largest exponent is two and there are three terms, so this is a quadratic trinomial.
The term with exponent ten determines the degree even though it is written second.
Integrated Math 2–3 Honors · Lesson Review · September 17, 2026
Polynomial Vocabulary, Classification, and Operations
Read the structure first: terms, degree, and leading coefficient tell you what a polynomial is—and like terms tell you how to simplify it.
01 · Watch
Lesson video
0:0001Polynomial Vocabulary and Operations0:0502What Is a Monomial?6:0703Build Polynomials from Monomials9:4804Terms, Coefficients, and Names14:1405Degree of a Term and a Polynomial19:1906Leading Term and Leading Coefficient21:5107Polynomial Names by Degree26:5108Classify by Degree and Terms32:2609Adding and Subtracting Polynomials37:3010Multiply by a Monomial41:3411Multiply Two Binomials44:3612Multiply Larger Polynomials52:4313Final Polynomial Product
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02 · Understand
Learning targets
- Distinguish monomials from expressions that contain disallowed exponents.
- Identify terms, coefficients, degree, leading term, and leading coefficient.
- Classify polynomials by degree and number of terms.
- Add, subtract, and multiply polynomials by combining like terms.
03 · Connect
Key ideas
Every expression below is rendered with KaTeX plus semantic MathML for clear reading and assistive technology.
- 01Monomial
- A number, a variable, or a product of numbers and variables whose variable exponents are whole numbers.
- 02Not a monomial
- Negative, fractional, or variable exponents fall outside the monomial definition.
- 03Term and coefficient
- Addition and subtraction separate terms; the numerical factor of a term is its coefficient.
- 04Degree
- For one term, add the variable exponents. For a polynomial, use the greatest term degree.
- 05Leading term
- Write in descending powers; the first term is the leading term and its coefficient is the leading coefficient.
04 · Apply
Worked examples
The examples follow the definitions, classifications, and operations used in the recorded board work.
Add
Combine only like terms
Line up equal powers of and add the coefficients of matching terms.
Subtract
Distribute the negative first
Every term in the second polynomial changes sign before like terms combine.
Distribute
Multiply a monomial by every term
Multiply coefficients and add exponents on matching bases.
Multiply
Every term meets every term
Distribute systematically, then combine the like terms in the middle.
Extend
A larger polynomial product
Organize the partial products by degree so no term is missed.
05 · Avoid
Common mistakes
Calling every expression a polynomial.
Check variable exponents first: they must be whole numbers.
Counting terms incorrectly.
Terms are separated by addition or subtraction, not by multiplication inside a term.
Using the first written exponent as the degree.
The degree comes from the greatest term degree, even when terms are out of order.
Combining unlike terms.
Terms combine only when their variable parts and exponents match.
Forgetting subtraction changes every sign.
Distribute the negative across the entire second polynomial.
Missing a product.
When multiplying polynomials, each term in one factor multiplies every term in the other.
06 · Check yourself
Quick check
Try each prompt before opening the worked answer.
1Why is the square root of x not a monomial?
shows that the square root is , which has a fractional exponent.
2How do you name a polynomial with degree two and three terms?
Quadratic trinomial, as in .
3What must happen before subtracting two polynomials?
Distribute the negative to every term in the second polynomial, then combine like terms: .
4What is the key check after multiplying polynomials?
Combine all like terms and write the result in descending degree, as in .
07 · Revisit
Transcript and captions
Search the corrected transcript for a definition or worked example, or download the caption files above.
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