College Algebra Vocab

REAL NUMBERS

REAL NUMBERS

all the numbers on the number line

RATIONAL NUMBERS

any number that can be rewritten as a fraction

IRRATIONAL NUMBERS

numbers that CANNOT be rewritten as a fraction. (non-terminating, non-repeating)

INTEGERS

any positive or negative whole number, including zero.

WHOLE NUMBERS

0,1,2,3,…

NATURAL NUMBERS

(also called the counting numbers) 1,2,3 …

IMAGINARY NUMBERS

the square root of a negative number, notated with i

COMPLEX NUMBERS

in the form a+bi where “a” is the real number and “bi” is the imaginary number

PRIME NUMBERS

any number that only has two factors: 1 and itself. A number in lowest terms

COMPOSITE NUMBERS

any number that has more than two factors. A number that can be rewritten as multiplication

BASE

In 2^5, 2 is the base

EXPONENT

In 2^5, 5 is the exponent. A shorthand notation for repeated multiplication

SQUARE ROOT

The reverse process of squaring a term

CUBE ROOT

The reverse process of cubing a term

RADICAL SIGN

the symbol used to indicate a root.

RADICAND

The term inside the radical sign

PERFECT SQUARE

a term times itself.

PERFECT CUBE

a term times itself three times.

ORDER OF OPERATIONS- FIRST

parentheses, brackets, absolute value, square root.

ORDER OF OPERATIONS- SECOND

Exponent

ORDER OF OPERATIONS- THIRD

M-multiplication and/or D-division (in order they appear left to right)

ORDER OF OPERATIONS- FOURTH

A-addition and/or S-subtraction (in order they appear left to right)

INVERSE OPERATIONS

are operations that “undo” each other. Add and subtract; multiply and divide; exponents and roots

ADDITION

“collect like terms”. Terms are alike when the variables are identical.

SUBTRACTION

“add the opposite”. The opposite of a number is called the additive inverse.

MULTIPLICITIVE INVERSE

Reciprocal of the fraction

COMPLEX FRACTION

a fraction which contains a fractional term in the numerator, denominator or both. This is unacceptable form so you must simplify by division.

UNDEFINED

the value of the denominator is 0. One cannot divide by 0!

COMMUNITIVE PROPERTY OF ADDITION

3+ 2 = 2 + 3

COMMUNITIVE PROPERTY OF MULTIPLICATION

(2)(3) = (3)(2)

ASSOCIATIVE PROPERTY OF ADDITION

2 + (3 + 4) = (2 + 3) + 4

ASSOCIATIVE PROPERTY OF MULTIPLICATION

2(3×4)=(2×3)4

ADDITIVE IDENTITY

2 + 0 = 2

MULTIPLICITIVE IDENTITY

2 (1) = 2

ADDITIVE INVERSE (ADD THE OPPOSITE)

2 + (-2) =0

MULTIPLICITIVE INVERSE (RECIPROCAL)

2(1/2)=1

DISTRIBUTIVE PROPERTY

This property is related to the operation of multiplication with addition/subtraction. Distributive means to multiply!

ALGEBRAIC EXPRESSION

is a collection of numbers, variables (letters), operation symbols and/or grouping symbols.

EXPRESSIONS ARE SIMPLIFIED

you perform the operation(s) you see according to PEMDAS.

SUBSTITUTE

replace the variable with an equivalent expression.

TERM

a number, a variable or the product of a number and variable(s). Example of terms: a, 7, 7a, 7ab

MONOMIAL

an algebraic expression consisting of ONE TERM that is a number(constant), a letter(variable), or the PRODUCT of number and letters.

BINOMIAL

a polynomial with exactly two terms: x + 5, a – b, 3xy + 7

TRINOMIAL

a polynomial with exactly three terms: a + b – c,

PERFECT SQUARE TRINOMIAL

a trinomial that factors into two binomials that are the same.

POLYNOMIAL

the SUM of many monomials. Examples of polynomial 5a + 3b –c + 4

COEFFICIENT

The number connected to the variable by multiplication.

DEGREE

the highest value of the exponent on the variable

FOIL

a way to remember how to multiply TWO BINOMIALS: First, Outer, Inner, Last

CONJUGATE

a new binomial that is formed by just changing the middle sign that connects the monomials. The conjugate of x - 3 is x + 3.

PRODUCT RULE

when one multiplies the SAME BASE, one just ADDS the exponents. (the base does not change)

POWER RULE

the exponents get multiplied together.

QUOTIENT RULE

when one divides the same base, just subtract the exponents.

ZERO EXPONENT

any base with an exponent of 0 has the value of 1

RATIONAL EXPONENT

an exponent that is a fraction

FACTORING

rewrite a polynomial as MULTIPLICATION

GCF

this is the largest divisor (factor) that all terms have in common.

DIFFERENCE OF PERFECT SQUARES

must be a binomial connected by subtraction, all numbers must be perfect squares and all exponents must be even.

TRINOMIAL

must have three terms written in descending order – a trinomial always factors into 2 binomials.

GROUPING

a method used to factor four monomials which have no GCF in common. Grouping always factors into two binomials.

SUM AND DIFFERENCE OF PERFECT CUBES

must a binomial connected by either addition or subtraction, numbers must be perfect cubes and exponents must be multiples of three. A perfect cube always factors into a binomial times a trinomial.

PRIME

an expression does not factor

EQUATION

a mathematical statement of equality. It is a collection of numbers, variables, operation symbols and an equal symbol!

FORMULA

a known relationship among quantities.

SOLUTION SET

answer to the equation that makes both sides of the equality balance. One checks the solution by evaluating. If the solution(s) do not check then one stated the there is NO SOLUTION

EXTRANEOUS SOLUTION

a solution that does not check in the original equation and therefore cannot be the answer.

LINEAR EQUATION

has the variable to the first power only, which means it can only have one solution.

RATIONAL EQUATION

an equation containing rational expressions (fractions). One solves a rational equation by multiplying each term by the LCD

QUADRATIC EQUATION

ax²+bx+c=0, must have 2 solutions

FACTORING

set equation =0, factor the expression and write two linear equations.

SQUARE ROOT METHOD

isolate the squared term, square root both sides and simplify the root.

COMPLETE THE SQUARE

the process to transform a binomial into a perfect square trinomial by adding on a perfect square number. To find the perfect square take half of coefficient in front of linear term and square it.

EXPONENTIAL EQUATION

y=b^x

SYSTEM OF EQUATIONS

consists of two or more equations. A solution of a system is a point (ordered pair or ordered triple) that checks in all equations.

CONSISTENT AND INDEPENDENT SYSTEM

when the two linear equations intersect, and the solution set is that point of intersection.

INCONSISTENT SYSTEM

when the two linear equations are parallel and there is NO solution set

DEPENDENT SYSTEM

when the two linear equations are identical and there are an infinite number of solutions.

HORIZONTAL LINE

If the equation ONLY has the variable y

VERTICAL LINE

If the equation ONLY has the variable x,

DIAGONAL LINE

If the equation has BOTH variables

SLOPE

referred to as “rise over run” Slope refers to the incline or steepness of a line.

PARALLEL LINES

Lines that will NEVER touch because they have the same slope

PERPENDICULAR LINES

two lines that intersect at a right angle; therefore they move in opposite directions which means the slope of perpendicular lines is the OPPOSITE RECIPROCALS of each other.

STANDARD FORM

Ax+By=C

“and”

Union

“or”

Intersection