Polynomials, Radical Equations, and Absolute Values

Vocabulary flashcards defining fundamental algebraic terms, polynomial characteristics, equation degrees, radical functions, and absolute value rules from the lecture.

Standard Form of a Polynomial

An expression arranged in descending powers of the variable set equal to zero, written as $a_n x^n + a_{n-1} x^{n-1} + \dots + a_0 = 0$.

Coefficients

The constant multiplier numbers (such as $a_n, a_{n-1}, \dots, a_0$) attached to variable terms in a polynomial.

Degree of a Polynomial

The highest power of any variable term present in a polynomial equation.

Linear Equation

A polynomial equation of degree $1$ that yields exactly $1$ solution.

Quadratic Equation

A polynomial equation of degree $2$ that yields up to $2$ solutions.

Quartic Equation

A polynomial equation of degree $4$ that yields up to $4$ solutions.

Radical Equation

An equation that contains at least one radical term (such as a square root) enclosing a variable expression.

Extraneous Solution

An extra solution obtained while solving (often after raising both sides to an even power) that fails to satisfy the original equation upon checking.

Absolute Value Equation Property

The algebraic principle stating that for an isolated expression $|u| = c$ where $c$ is a constant, $u = c$ or $u = -c$.