Polynomial Operations Notes
Polynomial comes from poly- (meaning “many”) and –nomial (in this case meaning “term”); thus, polynomial means “many terms”
A polynomial can have:
ConstantsVariablesExponents
Examples of polynomials
Terms: The number of terms is total number of a single number, variables, and/or number and variables multiplied together in an expression.
Term Names: There are special names for polynomials with 1, 2, or 3 terms:
MonomialBinomial Trinomial
(1 term) (2 terms) (3 terms)
Degree: A degree is the power of an exponent.
-If a term has two or more different variables multiplied together, then the degree is determined by the sum of all the exponents of the variables.
9
Polynomial: An expression of a sum of terms. Each + or – sign separates the terms. Each polynomial has a term number and degree.
Standard Form: This occurs when the polynomial’s terms are written from highest degree to the lowest degree. If more than one term has the same degree, but cannot be combined (different variables), then write in alphabetical order.
PolynomialPolynomial in Standard Form
Coefficient: The number in front of a term.
The coefficient is 1
Leading Coefficient: The coefficient of the highest degree term in a polynomial.
The leading coefficient is -9
Adding and Subtracting Polynomials: When combining like terms, each term must have the exact same variables and exponents on each variable. Note: when combining like terms, add/subtract the coefficients and keep the variables the exact same.
Multiplying Polynomials: You must distribute when multiplying. Any term can be multiplied to another. Thus, multiply the coefficients and add the exponents of same variables.
Naming Polynomials: Each polynomial can be classified by the number of terms and overall degree.
-The number of terms is easily identified. Remember, addition and subtraction separate each term.
-The degree of a polynomial is equal to the highest degree term. You do NOT add up all degrees to determine the degree of the polynomial.
Degree / Naming / Example / Terms / Term Specific Name0 / Constant / 4
1 / Linear /
2 / Quadratic /
3 / Cubic /
4 / Quartic /
5 / Quintic /
6+ / nth Degree Polynomial /
Examples of naming altogether: