Algebra Fundamentals and Operations

A set of 30 vocabulary flashcards covering algebraic definitions, classification of polynomials, laws of exponents, and special products based on the lecture notes.

Algebra

A branch of mathematics that uses letters or symbols to represent numbers in patterns, relationships, and equations to describe and solve real-life problems.

Algebraic expression

A mathematical phrase that contains numbers, variables, and operation symbols such as $+$, $-$ , $\times$, and $\div$, but does not have an equal sign.

Variable

A letter or symbol, such as $x$ or $y$, that represents an unknown number or a value that can change.

Constant

A fixed number, such as $5$, that cannot change its value.

Coefficient

The numerical factor of a term that contains a variable.

Numerical Coefficient

A number multiplied by a variable, such as the $3$ in the term $3x$.

Literal Coefficient

The letter used in an algebraic term to represent a number, such as the $x$ in the term $3x$.

Term

Each part of an algebraic expression that is separated by addition ($+$) or subtraction ($-$) symbols.

Like terms

Terms that have the same variables raised to the same exponents, though their numerical coefficients may differ.

Unlike terms

Terms that do not have the same variables or do not have the same variables raised to the same exponents.

Degree of a term

The sum of the exponents of the variables in a term; if a term has no variable, its degree is listed as $1$.

Simplify algebraic expressions

The process of combining like terms using addition or subtraction.

Polynomial

An expression with one or more terms involving variables raised to whole-number powers.

Degree of a polynomial

The highest degree of any of the terms within the polynomial after it has been simplified.

Modeling

The skill of translating real-life situations described in words into mathematical language and algebraic expressions.

Monomial

A type of polynomial that consists of only one term, such as $5xy$.

Binomial

A type of polynomial that consists of exactly two terms, such as $4a - 2b$.

Trinomial

A type of polynomial that consists of three terms, such as $x^2 + 3x - 6$.

Multinomial

Another term used to describe polynomials, specifically those with multiple terms like $2b^4 - 5b^3 - 4b + 1$.

Power of 1 Rule

An exponent rule stating that any base raised to the power of $1$ is equal to the base itself ($x^1 = x$).

Zero Exponent Rule

An exponent rule stating that any base raised to the power of $0$ is equal to $1$ ($x^0 = 1$).

Negative Exponent Rule

An exponent rule stating that a base with a negative exponent is equal to its reciprocal with a positive exponent ($x^{-1} = \frac{1}{x}$).

Product Rule

An exponent rule for multiplying powers with the same base, requiring the addition of the exponents ($x^m \cdot x^n = x^{m+n}$).

Quotient Rule

An exponent rule for dividing powers with the same base, requiring the subtraction of the exponents ($\frac{x^m}{x^n} = x^{m-n}$).

Power of a Power Rule

An exponent rule stating that to raise a power to another power, you multiply the exponents ($(x^m)^n = x^{mn}$).

Power of a Product Rule

An exponent rule stating that the power of a product is the product of the powers ($(xy)^n = x^n y^n$).

Power of a Quotient Rule

An exponent rule stating that the power of a quotient is the quotient of the powers ($(\frac{x}{y})^n = \frac{x^n}{y^n}$).

FOIL Method

A mnemonic standing for First, Outer, Inner, Last, used as a systematic order for multiplying two binomials.

Special Product

Polynomial expressions that follow recognizable patterns, such as the Square of a Binomial, to allow for faster calculation.