Variation and Polynomial Operations
When two quantities vary in a manner such that as one value increases, then the other value increases, it is called this.
Direct Variation
This is the theorem that if we evaluate a polynomial function at a particular value, c, then it is just the remainder of factoring out the binomial (x-c) from the polynomial.
The Remainder Theorem
The distance formula is derived by applying this theorem to the coordinates of two generic points on a plane.
The Pythagorean Theorem
This is the relationship between exponential and logarithmic functions.
Inverse Functions
A sequence that has a limited number of terms is called this.
Finite
When two quantities vary in a manner such that as one value increase the other decreases, it is called this.
Indirect
The Factor Theorem states that the binomial (x-r) is a factor of a polynomial if and only this is a solution to the equation P(x)=0. This is the word for that solution.
A root
This conic section is defined as the set of all points equidistant from a point called its center.
Circle
Exponential and Logarithmic functions are invertible because they have this property such that for every p and q in their domains, f(p)=f(q) if and only if p=q.
One-to-one
A sequence in which each successive term is defined by constant difference is called this
Arithmetic
This is the form in which we can represent any rational dividend.
The Division Algorithm
The is the number of roots that a polynomial with complex coefficients and degree n has.
n
This conic section is defined as the set of all points equidistant from a fixed line and a fixed point.
Parabola
Contrary to exponential functions, in logarithmic functions, if this parameter of the function is very larger, then the function grows much more slowly.
Base
A sequence in which each term is defined by a constant ratio is called this
We can use this algorithm to divide a polynomial by a binomial in the form (x-c)
Synthetic Division
This is the condition for the conjugate root theorem that states roots comes in conjugate pairs.
real coefficients
This conic section is defined as the set of all points in a plane such that the sum of the distances from any point to two given points is constant.
Ellipse
This is the amount of time it takes a substance to decay to half of its original mass.
Half Life
This is the condition on the common ratio of a geometric sequence for its infinite geometric series to have a limiting value
|r|<1
This is the set of numbers to which polynomials is "isomorphic" - meaning it shares the same algebraic structure under the operations of addition, subtraction, multiplication, and division.
Integers
This theorem states that all the potential roots of a polynomial with integral coefficients and of the type described by its name are found by taking the ratio of factors of leading coefficient and the constant term
The Rational Root Theorem
This conic section is defined as the set of all points in the plane such that the difference between the distances from a point to two fixed points is a given constant.
Hyperbola
This is the value that the function f(n)=(1+(1/n)n gets closer to as n gets closer to infinity.
e
This is the sequence that where to find the next term, the previous two terms are added together. It is neither algebraic or geometric.
Fibonacci Sequence