Analyze degree, leading coefficient, and end behavior. Math 30-1 Alberta.
Lesson 2.1 of Polynomial Functions in Math 30-1 — Alberta curriculum lessons.
Definition. A polynomial is an expression consisting of one or more algebraic terms with coefficients, constants, and variables raised to whole-number exponents.
Every polynomial is made up of terms. Each term consists of:
Coefficient: The number multiplying the variable (e.g., in 3x^2, the coefficient is 3). Variable: The letter representing an unknown value (commonly x, y, or other letters). Exponent: The power to which the variable is raised (must be a whole number: 0, 1, 2, 3, ...). Constant: A term without a variable (just a number).
Example Polynomial. 5x^3 - 2x^2 + 7x - 4
Breaking It Down.
For an expression to be a polynomial, it must follow these rules:
Key Rules.
Examples of polynomials vs. non-polynomials:
✓ These ARE Polynomials.
✗ These are NOT Polynomials.
Definition: Degree. The degree of a polynomial is the value of the greatest (highest) exponent of the variable.
Finding the Degree. Look for the term with the highest exponent:
Polynomials are also classified by how many terms they contain:
Monomial — 1 term.
Binomial — 2 terms.
Trinomial — 3 terms.
💡 Pro Tip. When working with polynomials, always identify the degree first. It gives you immediate insight into the polynomial's behavior and complexity!
Key Insight. The degree of a polynomial determines its fundamental shape and behavior. Let's explore each degree in detail, from simple to complex.
General Form. y = ax + b where a ≠ 0
Simplest Example. y = x (Linear Monomial)
General Form. y = ax^2 + bx + c where a ≠ 0
Simplest Example. y = x^2 (Quadratic Monomial)
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