College Algebra Vocab

all the numbers on the number line

any number that can be rewritten as a fraction

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

any positive or negative whole number, including zero.

0,1,2,3,…

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

the square root of a negative number, notated with i

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

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

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

In 2^5, 2 is the base

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

The reverse process of squaring a term

The reverse process of cubing a term

the symbol used to indicate a root.

The term inside the radical sign

a term times itself.

a term times itself three times.

parentheses, brackets, absolute value, square root.

Exponent

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

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

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

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

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

Reciprocal of the fraction

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

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

3+ 2 = 2 + 3

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

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

2(3×4)=(2×3)4

2 + 0 = 2

2 (1) = 2

2 + (-2) =0

2(1/2)=1

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

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

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

replace the variable with an equivalent expression.

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

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

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

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

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

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

The number connected to the variable by multiplication.

the highest value of the exponent on the variable

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

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

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

the exponents get multiplied together.

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

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

an exponent that is a fraction

rewrite a polynomial as MULTIPLICATION

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

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

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

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

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.

an expression does not factor

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

a known relationship among quantities.

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

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

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

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

ax²+bx+c=0, must have 2 solutions

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

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

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.

y=b^x

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

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

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

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

If the equation ONLY has the variable y

If the equation ONLY has the variable x,

If the equation has BOTH variables

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

Lines that will NEVER touch because they have the same slope

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.

Ax+By=C

Union

Intersection