Polynomials

Volume

Amount of 3d space occupied by an object / enclosed space within a container

Degree

The highest exponent of an in dependent variable.

Variable

A letter or symbol used to represent an unknown value in an expression or equation.

Coefficient

A number multiplied by a variable in an algebraic expression.

Relative maximum

The highest point in a particular section of a graph.

Constant

A fixed value that does not change, unlike a variable.

relative minimum

The lowest point in a particular section of a graph.

leading coefficient

the coefficient of the first term of a polynomial in standard form

Constant value

The value of a constant that doesn't consist of any variables.

Like terms

Expressions that contain the same variables to the same power

Expression

A mathematical phrase that contains operations, numbers, and/or variables.

Terms

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

Polynomial

a mathematical expression that is the sum of a 4 or more terms with positive exponents

Monomial

an expression with only one term

Binomial

An expression with two unlike terms

Trinomial

A polynomial with three unlike terms

standard form of a polynomial

a polynomial that is written with the terms in order from greatest degree to least degree.

Multiplicity

How many time a specific factor appears in a polynomial.

End Behavior

the behavior of the graph of a function as x approaches positive infinity or negative infinity

Polynomial Function

a function that is represented by a polynomial equation

Factor Theorem

A polynomial f(x) has a factor x - k if and only if f(k) = 0

Turning Points

A point where the function changes from increasing to decreasing (or vice versa).

of turning points

At most n−1 turning points.

Zero of a Polynomial Function

The value of x that makes the polynomial equal to zero.

x-intercepts on a graph

The points where the polynomial equals zero.

Surface Area

The total area of all outside faces of a three-dimensional object.

Function

A relationship between two variables for which each input corresponds to only 1 output value.

Integers

A whole number that can be positive, negative, or zero.

Distributive Property

Multiplying a number by a group of numbers added or subtracted together gives the same result as multiplying each number in the group individually and then combining the results.

Horizontal Intercept

A point on the graph of a function that crosses the x-axis.

Vertical Intercept

A point on the graph of a function that crosses the y-axis.

System of Equations

Two or more equations where the variable(s) represents the same unknown value.

Quadratic Equation

An equation that is equivalent to one of the form ax²+bx + c = 0, where a, b, and c are constants and a≠0.

Even-Degree Polynomials

A polynomial function whose leading term is raised to an even power; the graph's end behavior is the same on both sides.

Odd-Degree Polynomials

A polynomial function whose leading term is raised to an odd power; the graph's end behavior is opposite on both sides.

Point(s) of Intersection

The location where two or more functions cross on a graph.

Dividend

The number being divided.

Divisor

The number you are dividing by.

Quotient

The final answer to the division problem.

Remainder Theorem

States that dividing polynomial p(x) by (x - a) results in p(x) = (x - a)q(x) + r, where r is the remainder.

Leading Term

The first term of a polynomial when it is written in descending order of degree.