Comprehensive Guide to Dictionary SAT Advanced Math

Polynomial

An expression involving variables and coefficients with non-negative integer exponents.

Like Terms

Terms in a polynomial that have the same variable raised to the same exponent.

Distributive Property

A property indicating that a(b + c) = ab + ac.

Rational Exponents

Exponents that are expressed as a fraction, indicating roots and powers.

Product Rule

States that x^a * x^b = x^(a+b).

Power Rule

States that (x^a)^b = x^(ab).

Negative Exponent

Indicates that x^-a = 1/x^a.

Greatest Common Factor (GCF)

The largest factor that divides two or more expressions.

Difference of Squares

A factoring pattern represented by a^2 - b^2 = (a-b)(a+b).

Perfect Square Trinomials

Patterns represented by a^2 ± 2ab + b^2 = (a ± b)^2.

Rational Expressions

Fractions where the numerator and denominator are polynomials.

Extraneous Solutions

Solutions that do not satisfy the original equation, often from squaring both sides.

Quadratic Equation

An equation of the form ax^2 + bx + c = 0.

Zero Product Property

If ab = 0, then a = 0 or b = 0.

Quadratic Formula

A formula to find the solutions of a quadratic equation: x = (-b ± √(b² - 4ac)) / (2a).

Discriminant

The expression b² - 4ac in the quadratic formula that determines the nature of roots.

Radical Equations

Equations that involve radicals, requiring isolation and squaring to solve.

System of Equations

A set of equations with the same variables that can be solved together.

Substitution Method

A method of solving systems by isolating one variable and substituting it into another equation.

Elimination Method

A method used to eliminate one variable by adding or subtracting equations.

Vertex of a Parabola

The highest or lowest point of a quadratic function, found at (h, k) in vertex form.

Transformations of Functions

Changes applied to functions such as shifting, reflecting, or stretching.

Exponential Functions

Functions of the form f(x) = a * b^x, where b is the base.

Function Notation

A way to write functions that clearly indicates the independent variable.

Geometric Interpretation of Solutions

Visual representation of solutions to systems as intersection points of graphs.

Common Mistake: Dividing by Variable

An error where solutions may be lost by dividing by an unknown variable.