Introductory Algebra Vocabulary Review

30 vocabulary flashcards summarizing key algebraic terms and concepts covered in the lecture notes.

Natural Numbers

The counting numbers 1, 2, 3, … ; they do not include 0, negatives, fractions, or decimals.

Integers

All whole numbers and their opposites: … −3, −2, −1, 0, 1, 2, 3, …

Rational Numbers

Numbers that can be written as a fraction a⁄b where a and b are integers and b ≠ 0; includes terminating or repeating decimals.

Irrational Numbers

Real numbers that cannot be expressed as a fraction of integers; their decimals are non-terminating and non-repeating (e.g., √2, π).

Real Numbers

The set of all rational and irrational numbers; every point on the number line.

Opposite (Additive Inverse)

A number that when added to a given number equals 0; the opposite of a is −a.

Reciprocal (Multiplicative Inverse)

A number that when multiplied by a given non-zero number equals 1; the reciprocal of a⁄b is b⁄a.

Order of Operations

The agreed-upon sequence for simplifying expressions: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).

Polynomial in Standard Form

A polynomial written with terms in descending powers of its variable(s), each coefficient shown explicitly.

Prime Polynomial

A non-constant polynomial that cannot be factored over the integers into polynomials of lower degree.

Factoring Completely

Expressing a polynomial as a product of prime polynomials and constants with no further factoring possible.

Difference of Squares

A special product pattern: a² − b² = (a + b)(a − b).

Perfect Square Trinomial

A trinomial of the form a² ± 2ab + b², which factors to (a ± b)².

FOIL Method

Technique for multiplying two binomials: multiply First, Outer, Inner, Last terms and add results.

Quadratic Formula

For ax² + bx + c = 0, solutions are x = [−b ± √(b² − 4ac)] ⁄ (2a).

Solution Set

The set of all values that satisfy an equation or inequality.

Radical Expression

An expression containing a root symbol, such as √x or ³√(a + b).

Exact Answer

A solution left in symbolic form (e.g., √5, 3 + 2√3) rather than as a rounded decimal.

Simplified Fraction

A fraction whose numerator and denominator have no common factor other than 1.

Negative Exponent

Indicates reciprocal: a^(−n) = 1 ⁄ aⁿ for a ≠ 0.

Zero Exponent

For any non-zero base a, a⁰ = 1.

Positive Exponent

Indicates repeated multiplication: aⁿ = a · a · … · a (n times).

Product of Powers Rule

For same base, add exponents: a^m · a^n = a^(m+n).

Quotient of Powers Rule

For same base, subtract exponents: a^m ⁄ a^n = a^(m−n) (a ≠ 0).

Exponent of a Product Rule

(ab)^n = a^n b^n for all real numbers a, b.

Adding Fractions with Unlike Denominators

Rewrite each fraction with a common denominator, add numerators, then simplify.

Lowest Terms (Reduced Fraction)

A fraction in which the numerator and denominator share no common divisor other than 1.

Adding/Subtracting Polynomials

Combine like terms—terms with the same variables raised to the same powers.

Evaluate an Expression

Substitute given values for variables and perform the indicated operations.

Linear Equation

An equation of the first degree (ax + b = 0) whose graph is a straight line.