Learn polynomial terminology, degree, and classification. Grade 9 Alberta mathematics curriculum.
Lesson 5.1 of Polynomials in Grade 9 Math: Alberta curriculum lessons.
What Makes Each Polynomial Type Different?Polynomials can have one term or several terms.We name them based on how many terms they have.
Key Point. A term is a number, variable, or the product of both, separated by + or − signs.
A monomial has only one term.. ✅ Examples:3x7y²−4a³9Each example has a single term, no addition or subtraction signs.
A binomial has two terms joined by a plus (+) or minus (−) sign.. ✅ Examples:2x + 53y² − 4y−x³ + 2xEach one has exactly two separate parts (terms).
A trinomial has three terms.. ✅ Examples:x² + 3x + 24y³ − y + 1−2x² + 5x − 3Each term may have different exponents or coefficients, but they are all joined by + or −.
If an expression has four or more terms, we usually just call it a polynomial.. ✅ Examples:x³ + 2x² − 4x + 63y⁴ − 5y² + y − 7There's no special name beyond "polynomial". We simply describe it by the number of terms.
💡 Quick Counting Method. You can quickly count the number of terms by counting how many + or − signs appear (each separates terms).
For example:. 4x³ + 3x² − x + 5has 4 terms, so it's a polynomial.
A binomial is a polynomial with two terms.. For example:2x + 5If we write it as5 + 2xit still means the same thing. Both expressions are equivalent.
Key Point. The order of the terms doesn't matter as long as the coefficients, variables, and exponents are the same.
This same idea applies to any polynomial with more terms.
4x² + 2x + 7This is a polynomial because: It has three terms separated by + signs.; The exponents (2 and 1) are whole numbers.; There are no fractions or roots involving variables.
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