Polynomial Functions and Operations

These flashcards cover definitions and concepts related to polynomials and their operations as discussed in the lecture notes.

Monomial

A number, variable, or a product of numbers and variables.

Polynomial

The sum or difference of multiple monomials.

Leading Coefficient

The coefficient of the term with the highest degree in a polynomial.

Degree of a Polynomial

The highest exponent in a polynomial.

Combining Like Terms

The process of simplifying expressions by adding or subtracting similar terms.

Zeros of a Polynomial

The values of x that make the polynomial equal to zero.

Turning Points

Points at which a polynomial function changes direction.

End Behavior

The behavior of a polynomial function as x approaches positive or negative infinity.

Even Degree Polynomial

A polynomial whose highest exponent is even.

Odd Degree Polynomial

A polynomial whose highest exponent is odd.

Multiplicity

The number of times a zero occurs in a polynomial.

Factor Theorem

States that if a polynomial f(x) has a zero at x = k, then (x - k) is a factor of f(x).

Difference of Squares

The algebraic identity a² - b² = (a - b)(a + b).

Sum of Cubes

The algebraic identity a³ + b³ = (a + b)(a² - ab + b²).

Difference of Cubes

The algebraic identity a³ - b³ = (a - b)(a² + ab + b²).

GCF (Greatest Common Factor)

The largest factor that divides two or more numbers.

Synthetic Division

A shorthand method of polynomial long division.

Graphing Polynomial Functions

The process of plotting points to visualize a polynomial function.

Standard Form of a Polynomial

A way of writing a polynomial where the terms are ordered by decreasing degree.

Polynomial Function

A function that can be represented by a polynomial equation.