1. Introduction & Key Vocabulary
A polynomial is an algebraic expression consisting of variables, coefficients, and exponents,
combined using only addition, subtraction, and multiplication. The exponents of the variables
must be whole numbers.
● Terms: Parts of the expression separated by $+$ or $-$ signs.
● Coefficients: The numerical coefficients multiplying the variables.
● Leading Coefficient: The coefficient of the term with the highest exponent.
● Constant Term: A number without a variable.
● Degree: The highest exponent of the variable in the polynomial, which determines the
maximum number of roots it can have.
2. Classifying Polynomials
Polynomials are typically classified in two ways to easily describe them:
By Degree (Highest Power) Name Example
Degree 0 Constant $f(x) = 6$
Degree 1 Linear $f(x) = ax + b$
Degree 2 Quadratic $f(x) = ax^2 + bx + c$
Degree 3 Cubic $f(x) = ax^3 + bx^2 + cx + d$
By Number of Terms Name Example
1 Term Monomial $5x$
A polynomial is an algebraic expression consisting of variables, coefficients, and exponents,
combined using only addition, subtraction, and multiplication. The exponents of the variables
must be whole numbers.
● Terms: Parts of the expression separated by $+$ or $-$ signs.
● Coefficients: The numerical coefficients multiplying the variables.
● Leading Coefficient: The coefficient of the term with the highest exponent.
● Constant Term: A number without a variable.
● Degree: The highest exponent of the variable in the polynomial, which determines the
maximum number of roots it can have.
2. Classifying Polynomials
Polynomials are typically classified in two ways to easily describe them:
By Degree (Highest Power) Name Example
Degree 0 Constant $f(x) = 6$
Degree 1 Linear $f(x) = ax + b$
Degree 2 Quadratic $f(x) = ax^2 + bx + c$
Degree 3 Cubic $f(x) = ax^3 + bx^2 + cx + d$
By Number of Terms Name Example
1 Term Monomial $5x$
