Polynomials • Topic 1 of 4

Polynomial Terminology

A polynomial is a sum of terms, each a number times a variable raised to a whole-number power, such as 3x² − 5x + 2. The degree is the highest exponent present; the leading coefficient is the number on that highest-degree term; the constant term has no variable. Polynomials are named by number of terms (monomial, binomial, trinomial) and by degree (linear = 1, quadratic = 2, cubic = 3). Writing a polynomial in standard form means ordering terms from highest to lowest degree. Knowing this vocabulary lets you read SAT questions about degree, end behaviour and number of terms precisely.

✅ Solved examples

1. What is the degree of 4x³ − 2x + 7?
The highest exponent is 3, so the degree is 3.
2. What is the leading coefficient of 5x² + 3x − 1?
The highest-degree term is 5x², so the leading coefficient is 5.
3. How many terms does 2x² + 3x + 4 have?
Three terms, so it is a trinomial.
4. What is the constant term of 7x² − 4x + 9?
The term with no variable is 9.

✏️ Practice — try these, take hints as needed

1. What is the degree of 6x⁴ + x² − 3?
Find the highest exponent.
It is 4.
—
4.
2. What is the leading coefficient of −3x³ + 2x?
Highest-degree term is −3x³.
Take its coefficient with sign.
—
−3.
3. How many terms does 5x − 2 have?
Count parts separated by + / −.
Two.
—
Two (a binomial).
4. What is the constant term of 2x³ + x − 6?
Term with no variable.
Include the sign.
—
−6.
5. What is the degree of the monomial 9x⁵?
Read the exponent.
—
—
5.

📝 Topic test — 8 questions

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