Introduction to Linear Polynomials

This flashcard set covers the vocabulary and foundational concepts of linear polynomials, including types of polynomials, components of algebraic expressions, and the properties of linear growth, decay, and relationships.

Algebraic Expression

A combination of numbers, variables, and operation symbols.

Variables

Letter-numbers used in algebraic expressions to represent unknown values, such as $x$ and $y$.

Terms

The parts of an algebraic expression separated by addition or subtraction; for example, in $4x + 5y + 3$, the terms are $4x$, $5y$, and $3$.

Coefficients

The numerical factors of the variable terms; for example, in the expression $4x + 5y$, the numbers $4$ and $5$ are the coefficients.

Constant

A fixed numerical value in an expression that does not change, such as the number $3$ in $4x + 5y + 3$.

Univariate Polynomials

Algebraic expressions involving only one variable and its powers, also called one-variable polynomials.

Degree

The highest power of the variable in a polynomial.

Cubic Polynomial

A polynomial with a degree of $3$, such as $5y^3 + y^2 + 2y - 1$.

Quadratic Polynomial

A polynomial with a degree of $2$, such as $x^2 + 5x + 1$.

Linear Polynomial

A polynomial with a degree of $1$, such as $3z + 7$.

Constant Polynomial

A polynomial with a degree of $0$, such as the number $8$ (which can be written as $8x^0$).

Linear Equation

A mathematical statement formed by equating a linear polynomial in one variable to a constant.

Function

An input-output process where an expression (like $2x + 3$) produces a specific output for every input value of the variable $x$.

Linear Pattern

A sequence of numbers where the difference between two consecutive terms is constant.

Linear Growth

A pattern where a quantity increases by a fixed, constant amount over equal intervals.

Linear Decay

A pattern where a quantity decreases by a fixed, constant amount over equal intervals.

Linear Relationship

A relationship between two variables $x$ and $y$ that can be expressed in the form $y = ax + b$ and represented by a straight line.

Slope ($a$)

The constant $a$ in the equation $y = ax + b$ representing the steepness of the line or the constant difference between terms.

y-intercept ($b$)

The value $b$ in the equation $y = ax + b$, representing the distance from the origin where the line cuts the y-axis at the point $(0, b)$.

Parallel Lines

Lines that have equal slopes ($a$) but different y-intercepts ($b$).