Math 3 Vocab. Ch.7

Irrational Root Theorem

he Conjugate Roots Theorem for Irrational Roots states that for a polynomial f ( x ) with integer coefficients, if a root of the equation f ( x ) = 0 is expressed as a + α , where a ∈ Q and α ∈ R − Q are rational and is irrational, then a − α is also a root of the equation.

Numerator

he number above the line in a common fraction showing how many of the parts indicated by the denominator are taken, for example, 2 in 2/3.

Complex Number

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, satisfying the equation i2 = −1. In this expression, a is the real part and b is the imaginary part of the complex number.

Rational Solutions

A number that can be made by dividing two integers. (Note: integers have no fractions.) The word comes from "ratio". Examples: • 1/2 is a rational number (1 divided by 2, or the ratio of 1 to 2)

Polynomial function

A polynomial function has the form , where are real numbers and n is a nonnegative integer. In other words, a polynomial is the sum of one or more monomials with real coefficients and nonnegative integer exponents. The degree of the polynomial function is the highest value for n where an is not equal to 0.

Product

A product in math is defined as the answer of an equation in which two or more variables are multiplied. In other terms, a product is the answer to any multiplication problem.

Fundamental Theorem of Algebra

Definition of fundamental theorem of algebra. : a theorem in algebra: every equation which can be put in the form with zero on one side of the equal-sign and a polynomial of degree greater than or equal to one with real or complex coefficients on the other has at least one root which is a real or complex number.

Complex Conjugate Root Theorem

In mathematics, the complex conjugate root theorem states that if P is a polynomial in one variable with real coefficients, and a + bi is a root of P with a and b real numbers, then its complex conjugate a − bi is also a root of P.

Multiplicity

In mathematics, the multiplicity of a member of a multiset is the number of times it appears in the multiset. For example, the number of times a given polynomial equation has a root at a given point.

Synthetic Division

Synthetic division is a shorthand, or shortcut, method of polynomial division in the special case of dividing by a linear factor -- and it only works in this case. Synthetic division is generally used, however, not for dividing out factors but for finding zeroes (or roots) of polynomials.

Rational Zero Theorem

The Rational Zeros Theorem states: If P(x) is a polynomial with integer coefficients and if is a zero of P(x) ( P( ) = 0 ), then p is a factor of the constant term of P(x) and q is a factor of the leading coefficient of P(x) .

Greatest Common Factor

The highest number that divides exactly into two or more numbers. When we find all the factors of two or more numbers, and some factors are the same ("common"), then the largest of those common factors is the Greatest Common Factor. Abbreviated "GCF".

Root

The root of a number x is another number, which when multiplied by itself a given number of times, equals x. For example the second root of 9 is 3, because 3x3 = 9. The second root is usually called the square root. The third root is susually called the cube root See Root (of a number).

Factor

a number or quantity that when multiplied with another produces a given number or expression.

Coefficients

a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g., 4 in 4x y).

Quotient

a result obtained by dividing one quantity by another. 2. a degree or amount of a specified quality or characteristic. "the increase in Washington's cynicism quotient"

Zeroes of a function

n mathematics, a zero, also sometimes called a root, of a real-, complex- or generally vector-valued function f is a member x of the domain of f such that f(x) vanishes at x; that is, x is a solution of the equation f(x) = 0. In other words, a "zero" of a function is an input value that produces an output of zero (0).

Denominator

the number below the line in a common fraction; a divisor. a figure representing the total population in terms of which statistical values are expressed.