Algebra
Algebra is the branch of mathematics that uses letters and symbols to represent numbers and quantities in equations and formulas. From solving simple linear equations to factoring polynomials and working with quadratic functions, algebra is the foundation for all higher mathematics. This page collects every algebra term, formula, and concept covered on Mathwords.
Key Concepts
Polynomial Facts
Polynomial Facts is a collection of essential theorems and properties about polynomials of the form p(x) = aₙxⁿ + aₙ₋...
Factoring Rules
Factoring rules are a collection of algebra formulas that allow you to rewrite a polynomial as a product of simpler e...
Set-Builder Notation
Set-builder notation is a compact way to describe a set by stating a rule or condition that its elements must satisfy...
Focal Radius
Focal radius is a term with two common meanings: (1) the distance from the center of an ellipse or hyperbola to a foc...
Absolute Value Rules
Absolute value rules are the algebraic properties that govern how absolute values interact with arithmetic operations...
ARC
Average rate of change is the change in the output of a function divided by the change in the input over a given inte...
Average Rate of Change
Average rate of change is the change in the output of a function divided by the change in the input over a given inte...
Synthetic Division
Synthetic division is a streamlined method for dividing a polynomial by a linear expression of the form x − c, using ...
Dilation of a Graph
Dilation of a graph is a transformation that stretches or compresses a graph by multiplying all x-coordinates or all ...
Equation of a Line
Equation of a line is an algebraic equation whose solutions form a straight line when plotted on a coordinate plane. ...
Inverse of a Matrix
The inverse of a matrix is a square matrix $A^{-1}$ that, when multiplied by the original matrix $A$, produces the id...
Matrix Inverse
The inverse of a matrix is a square matrix $A^{-1}$ that, when multiplied by the original matrix $A$, produces the id...
All Algebra Terms (497)
- Abscissa
- Absolute Value
- Absolute Value Equation
- Absolute Value Function
- Absolute Value Inequality
- Absolute Value Rules
- Acceleration
- Accuracy
- Additive Inverse of a Matrix
- Algebra
- Amortization
- Analytic Geometry
- Analytic Methods
- Annuity
- ARC
- Argand Plane
- Argument of a Function
- Arithmetic Progression
- Arithmetic Series
- Asymptote
- Augmented Matrix
- Axes
- Axis of Reflection
- Axis of Symmetry
- Axis of Symmetry of a Parabola
- Back Substitution
- Bar Graph
- Base of an Exponential Expression
- Bayes' Theorem
- Biconditional
- Big O Notation
- Binary / Base 2
- Binomial Coefficients
- Binomial Coefficients in Pascal's Triangle
- Binomial Theorem
- Bivariate Data
- Boolean Logic
- Cartesian Coordinates
- Cartesian Form
- Cartesian Plane
- Categorical Data
- Ceiling Function
- Change of Base Formula
- Check a Solution
- Chi-Square Test
- Circle Graph (Pie Chart)
- Closed Interval
- Coefficient
- Coefficient Matrix
- Coefficient of Determination (R²)
- Column of a Matrix
- Combination
- Combination Formula
- Combinatorics
- Common Logarithm
- Common Ratio
- Compatible Matrices
- Completing the Square
- Complex Conjugate
- Complex Fraction
- Complex Number Formulas
- Complex Numbers
- Composite
- Composition
- Compound Inequality
- Compound Interest
- Compounded Continuously
- Compression
- Compression of a Graph
- Compute
- Conditional Equation
- Conditional Inequality
- Confidence Interval
- Conic Sections
- Conjugate Pair Theorem
- Conjugates
- Consistent System of Equations
- Constant
- Constant Function
- Constant of Proportionality
- Constant Polynomial
- Continued Sum
- Continuity at a Point
- Contrapositive
- Converge
- Convergent Sequence
- Convergent Series
- Coordinate Grid
- Coordinates
- Correlation vs. Causation
- Cost Function
- Cramer’s Rule
- Cross Multiplication
- Cross Section
- Cube Root
- Cubic Polynomial
- Cumulative Frequency
- Decay Factor
- Decimal
- Decreasing Function
- Degenerate
- Degree of a Polynomial
- Degree of a Term
- Delta (Δ δ)
- Dependent Events
- Dependent Variable
- Descartes' Rule of Signs
- Determinant
- Diagonal Matrix
- Difference of Cubes
- Difference of Squares
- Difference Quotient
- Dilation
- Dilation of a Graph
- Dimensional Analysis
- Dimensions
- Dimensions of a Matrix
- Direct Proportion
- Directrix of a Parabola
- Discriminant of a Quadratic
- Distance Formula
- Distinct
- Distribute
- Distributing Rules
- Distributive Property
- Diverge
- Divergent Sequence
- Divergent Series
- Divisibility Rules
- Domain
- Domain of Definition
- Dot Plot
- Double Cone
- Double Root
- Doubling Time
- e
- Eigenvalue
- Eigenvector
- Element of a Matrix
- Ellipse
- Empirical Rule (68-95-99.7 Rule)
- End Behavior
- Epsilon-Delta Definition
- Equation
- Equation of a Line
- Equation vs. Expression
- Equivalent Systems of Equations
- Euclidean Distance
- Evaluate
- Even Function
- Existential Quantifier
- Experimental Probability
- Explicit Formula of a Sequence
- Exponent
- Exponent Rules
- Exponential Decay
- Exponential Equation
- Exponential Function
- Exponential Growth
- Exponential Regression
- Exponentiation
- Expression
- Extraneous Solution
- Extrapolation
- Extrema
- Extreme Values of a Polynomial
- Extremum
- Factor of a Polynomial
- Factor Theorem
- Factored Form
- Factorial
- Factoring Rules
- Falling Bodies
- Fibonacci Sequence
- Flip
- Floor Function
- Focal Radius
- Foci of a Hyperbola
- Foci of an Ellipse
- Focus
- Focus of a Parabola
- FOIL Method
- Formula
- Fractional Equation
- Fractional Exponents
- Fractional Expression
- Frequency Table
- Function
- Function Notation
- Function Operations
- Fundamental Counting Principle
- Fundamental Theorem of Algebra
- Fundamental Theorem of Arithmetic
- Future Value
- Gambling Odds
- Gaussian Elimination
- GCF
- General Form for the Equation of a Line
- Geometric Mean
- Geometric Progression
- Geometric Series
- Glide
- Golden Mean
- Golden Spiral
- Graph of an Equation or Inequality
- Graph Theory
- Graphic Methods
- Gravity
- Growth Factor
- Half-Closed Interval
- Half-Life
- Harmonic Mean
- Harmonic Progression
- Harmonic Series
- Hexadecimal
- Histogram
- Horizontal Asymptote
- Horizontal Compression
- Horizontal Dilation
- Horizontal Hyperbola
- Horizontal Line Equation
- Horizontal Line Test
- Horizontal Parabola
- Horizontal Reflection
- Horizontal Shift
- i
- Identity (Equation)
- Identity Matrix
- Identity of an Operation
- Identity Property of Addition
- Identity Property of Multiplication
- Imaginary Numbers
- Imaginary Part
- Improper Rational Expression
- Inconsistent System of Equations
- Increasing Function
- Independent Variable
- Inequality
- Inequality Rules
- Infinite Geometric Series
- Infinite Series
- Interest
- Interpolation
- Interval
- Interval Notation
- Inverse
- Inverse Function
- Inverse of a Matrix
- Inverse Operations
- Inverse Proportion
- Invertible Matrix
- Joint Variation
- Latus Rectum
- Law of Large Numbers
- LCM
- Leading Coefficient
- Leading Coefficient Test
- Leading Term
- Least Common Denominator
- Like Terms
- Limit Definition of Derivative
- Limit Laws
- Line of Best Fit
- Linear
- Linear Combination
- Linear Equation
- Linear Factorization
- Linear Inequality
- Linear Polynomial
- Linear Programming
- Linear Regression
- Linear System of Equations
- Literal Equation
- Locus
- Logarithm
- Logarithm Rules
- Logarithmic Equation
- Logical Equivalence
- Logistic Growth
- Long Division of Polynomials
- Magnitude
- Main Diagonal of a Matrix
- Major Axis of a Hyperbola
- Major Axis of an Ellipse
- Major Diameter of an Ellipse
- Margin of Error
- Mathematical Model
- Mathematical Model
- Matrix
- Matrix Addition
- Matrix Multiplication
- Matrix Subtraction
- Matrix Transformation
- Mean
- Mean Absolute Deviation (MAD)
- Mean of a Random Variable
- Member of an Equation
- Midpoint
- Midpoint Formula
- Minor Axis of a Hyperbola
- Minor Axis of an Ellipse
- Minor Diameter of an Ellipse
- Mode
- Monomial
- Multiplicity
- Multivariable
- Natural Logarithm
- Negation
- Negative Exponents
- Negative Reciprocal
- Net (Geometry)
- No Slope
- Noninvertible Matrix
- Nonreal numbers
- Nontrivial
- Normal Distribution
- nth Root
- nth Root Rules
- Null Hypothesis
- Number Line
- Oblique
- Oblique Asymptote
- Odd Function
- One Dimension
- One-to-One Function
- Open Interval
- Order of Operations (PEMDAS)
- Ordinate
- Origin
- Outlier Rule (1.5 x IQR)
- Oval
- Overdetermined System of Equations
- p-value
- Parallel Slopes
- Parameter (Statistics)
- Parent Functions
- Partial Fractions
- Per Annum
- Percent / Percentage
- Percent Change
- Percent Error
- Perfect Square Trinomial
- Permutation
- Permutation Formula
- Perpendicular Slopes
- Piecewise Function
- Piecewise Linear Function
- Place Value
- Point of Symmetry
- Point-Slope Equation of a Line
- Polynomial
- Polynomial Facts
- Polynomial Function
- Polynomial Inequality
- Positive Series
- Precision
- Present Value
- Principal
- Probability Distribution
- Proper Rational Expression
- Proportion
- Proportional
- Quadrants
- Quadratic
- Quadratic Equation
- Quadratic Formula
- Quadratic Function
- Quadratic Polynomial
- Quadratic Regression
- Quantitative Data
- Quartic Polynomial
- Quintic Polynomial
- Radical
- Radical Equation
- Radicand
- Random Sample
- Random Variable
- Range
- Rate of Change
- Rational Function
- Rational Numbers
- Rational Root Theorem
- Rationalizing the Denominator
- Real Numbers
- Real Part
- Recursion
- Recursive Formula of a Sequence
- Reduced Row-Echelon Form of a Matrix
- Regression Line
- Relation
- Relative Frequency
- Relatively Prime
- Remainder
- Remainder Theorem
- Residual Plot
- Restricted Domain
- Restricted Function
- Rigid Transformation
- RMS
- Root of a Number
- Root of an Equation
- Rotation
- Row of a Matrix
- Row Operations
- Row Reduction
- RPM
- Sampling
- Sampling Bias
- Satisfy
- Scalar Multiplication of a Matrix
- Scale Factor
- Scatterplot
- Scientific Notation
- Sequence
- Series
- Set-Builder Notation
- Sigmoid Function
- Significance Level (Alpha)
- Simple Interest
- Simplify
- Simultaneous Equations
- Slope Formula
- Slope of a Line
- Slope-Intercept Equation of a Line
- Solution
- Solve
- Solve Analytically
- Solve Graphically
- Speed
- Square Matrix
- Square Root
- Square Root Rules
- Square System of Equations
- Squeeze Theorem
- Standard Deviation
- Standard Form of a Quadratic
- Statistic
- Step Function
- Strict Inequality
- Sum of Cubes
- Surd
- Symmetric
- Symmetric about the Origin
- Symmetric about the x-axis
- Symmetric about the y-axis
- Synthetic Division
- Synthetic Substitution
- System of Inequalities
- Term
- Theoretical Probability
- Time Series
- Transformations
- Translation (Geometry)
- Transpose of a Matrix
- Tree Diagram
- Triangle Inequality with Absolute Value
- Trinomial
- Triple Root
- Trivial
- Truth Table
- Two Dimensions
- Two Intercept Form for the Equation of a Line
- Two-Way Table
- Type I Error
- Type II Error
- Underdetermined System of Equations
- Uniform
- Unit Rate
- Univariate Data
- Universal Quantifier
- Variable
- Variance
- Vector Space
- Velocity
- Vertex Form
- Vertex of a Hyperbola
- Vertex of a Parabola
- Vertex of an Ellipse
- Vertical Asymptote
- Vertical Compression
- Vertical Dilation
- Vertical Line Equation
- Vertical Line Test
- Vertical Reflection
- Vertical Shift
- Weighted Average
- Weighted Mean
- x-axis
- x-intercept
- y-axis
- y-intercept
- Z-Score
- Zero Matrix
- Zero of a Function
- Zero Product Property
- Zero Property of Multiplication
- Zero Slope
Frequently Asked Questions
What is algebra?
Algebra is a branch of mathematics that uses variables (letters like x and y) to represent unknown values. It involves solving equations, working with expressions, and understanding functions and their graphs.
What topics are covered in Algebra 1 vs Algebra 2?
Algebra 1 covers linear equations, inequalities, systems of equations, polynomials, and basic factoring. Algebra 2 extends into quadratic functions, exponential and logarithmic functions, complex numbers, and sequences and series.
Why is algebra important?
Algebra develops logical thinking and problem-solving skills. It is essential for careers in science, engineering, medicine, economics, and technology. Nearly every standardized math test (SAT, ACT, GRE) emphasizes algebraic reasoning.