Algebra Review: Linear Equations, Polynomials, and Factoring

Vocabulary flashcards covering core algebra concepts from lecture notes, including linear equations, slopes, polynomial classification, special product formulas, and GCF factoring.

Slope of a Horizontal Line

A line characterized by an equation of the form $y = c$, where the vertical change is zero, yielding a slope of $m = 0$.

Slope of a Vertical Line

A line characterized by an equation of the form $x = c$, where the horizontal change is zero, resulting in an undefined slope.

Slope Formula

The mathematical formula $m = \frac{y_2 - y_1}{x_2 - x_1}$, used to determine the slope or rate of change between two coordinates $(x_1, y_1)$ and $(x_2, y_2)$.

Slope-Intercept Form

The linear equation format $y = mx + b$, where $m$ represents the slope and $(0, b)$ represents the coordinates of the $y\text{-intercept}$.

Binomial

A polynomial algebraic expression containing exactly two terms, such as $x^2 - 4xy$.

Degree of a Polynomial

The highest exponent or highest sum of variable exponents among the individual terms in a polynomial expression.

Combining Like Terms

The algebraic procedure of simplifying an expression by adding or subtracting coefficients of terms with identical variable factors raised to identical powers.

Polynomial Subtraction

The operation of subtracting one polynomial from another by distributing the negative sign across each term in the subtrahend and subsequently grouping like terms.

FOIL Method

A mnemonic method used to multiply two binomials by summing the products of their First terms, Outer terms, Inner terms, and Last terms.

Square of a Binomial Formula

The special product identity stating that $(a + b)^2 = a^2 + 2ab + b^2$ and $(a - b)^2 = a^2 - 2ab + b^2$.

Product of a Sum and a Difference

The special product formula $(a + b)(a - b) = a^2 - b^2$, which results in a difference of squares.

Greatest Common Factor (GCF)

The highest common numerical factor combined with the lowest shared exponent of each variable across all terms in a polynomial expression.

Factoring a Common Binomial Factor

The process of extracting a shared two-term expression from multiple terms using the distributive property, such as rewriting $x(x + 7) + 2(x + 7)$ as $(x + 7)(x + 2)$.