Section 7.1: Introduction to Polynomials
A polynomial is an expression made up of variables, coefficients, and exponents that are non-negative integers. Polynomials are classified by degree and number of terms.
Polynomial Terms:
\( 5x^3 \) is a term with coefficient 5, variable \( x \), and exponent 3.
\( -2xy^2 \) is a term with coefficient -2, variables \( x \) and \( y \), and exponents 1 and 2.
Example 1
Classify each polynomial:
(a) \( 3x^2 + 5x - 7 \)
(b) \( 4y^3 \)
(a) Trinomial of degree 2
(b) Monomial of degree 3
Practice Problems
- Identify the degree and type (mono-, bi-, tri-) of \( 7x^4 - 3x^2 + 1 \).
- Identify the degree and type of \( -5y^3 \).
- Write a polynomial of degree 2 with three terms.
- Write a monomial with degree 5.
- Classify: \( x^3 + 4x^2 - x + 6 \)