Algebra Chapter 2 Vocabulary

Front 1

Complex Conjugate

Back 1

complex number that when multiplied by another complex number produces a value that is wholly real

Front 2

Complex Conjugate Theorum

Back 2

Let p(x) be a polynomial with real coefficients. If a+bi is a root of the equation p(x)=0, where a and b are real and b≠0, then a-bi is also a root of the equation.

Front 3

Depressed Polynomial

Back 3

result of dividing a polynomial by its binomial factors

Front 4

End Behavior

Back 4

behavior of the graph as x approaches positive or negative infinity

Front 5

Even-Degree Polynomial Function

Back 5

polynomial function in which the highest exponent is an even number; ends will extend in same direction

Front 6

Factor of a Polynomial

Back 6

any polynomial that divides evenly into the function

Front 7

Factor Theorum

Back 7

The binomial x-a is a factor of the polynomial p(x) if and only if p(a)=0.

Front 8

Fundamental Theorum of Algebra

Back 8

If p(x) is a polynomial function of degree n≥1 with complex coefficients, then the related equation p(x)=0 has at least one complex solution.

Front 9

Integer

Back 9

number that is not a fraction or decimal

Front 10

Integral Zero Theorum

Back 10

If the coefficients of a polynomial function are integers such that an=1and a0≠0, then any rational zeros of the function must be factors of a0.

Front 11

Irrational Root Theorum

Back 11

If a polynomial p(x) has rational coefficients and a+b√c is a root of the polynomial equation p(x)=0, where a and b are rational and √c is irrational, then a-b√c is also a root of p(x)=0.

Front 12

Local Maximum

Back 12

greatest value of a function for a particular interval of a function

Front 13

Local Minimum

Back 13

least value of a function for a particular interval of the function

Front 14

Multiplicity(of a zero)

Back 14

number of times a zero of a polynomial function occurs

Front 15

Odd-Degree Polynomial Function

Back 15

polynomial in which the highest exponent is an odd number. One end will extend downward.

Front 16

Polynomial Function

Back 16

function of the general form f(x)=anXn + an-1Xn-1 + ......., where a1 is a rational number, an≠0, and n is a nonnegative integer and the highest degree of the polynomial

Front 17

Rational Root Theorum

Back 17

If the polynomial p(x) has integer coefficients, then every rational root of the polynomial equation p(x)=0 can be written in the form p\q, where p is the factor of the leading coefficient of p(x).

Front 18

Relative Maximum

Back 18

greatest value of a function for a particular interval of the function

Front 19

Relative Minimum

Back 19

least value of a function for a particular interval of the function

Front 20

Remainder Theorum

Back 20

For a polynomial p(x) and a number a, dividing p(x) by x-a results in a remainder of p(a), so p(a)=0 if and only if (x-a) is a factor of p(x).

Front 21

Repeated Root

Back 21

polynomial function with a root that occurs more than once

Front 22

Root

Back 22

the x-intercept of a function; also known as zero

Front 23

Synthetic Division

Back 23

shorthand of dividing a polynomial by a linear binomial

Front 24

Synthetic Substitution

Back 24

process of using synthetic division to evaluate a function by using only the coefficients

Front 25

Turning Point

Back 25

point where the graph of the function changes direction from sloping upward to sloping downward or vice versa

Front 26

Zero

Back 26

the x-intercept of a function; also known as a root