Algebra Calculators

30 free algebra calculators in Math.

Completing the SquareRewrite ax²+bx+c into vertex form a(x−h)²+k and identify the vertex coordinates.
Composite Function CalculatorCompute (f∘g)(x) = f(g(x)) by evaluating two functions in sequence at a given x value.
Cubic Equation SolverFind all three roots of ax³+bx²+cx+d=0 using the depressed-cubic method, including complex roots.
Domain CalculatorEstimate the domain of f(x) by sampling the expression parser across a wide range of x values.
Exponent CalculatorRaise any base to any power, including negative and fractional exponents.
FOIL CalculatorMultiply two binomials (ax+b)(cx+d) using the FOIL method with step-by-step breakdown.
Function CalculatorEvaluate a mathematical function f(x) at a given value using the built-in expression parser.
Function OperationsCompute (f+g)(x), (f−g)(x), (f·g)(x) and (f/g)(x) for two expressions at a given x.
Half-Life CalculatorSolve exponential decay for half-life, mean lifetime, decay constant or remaining quantity.
Inverse Function CalculatorNumerically approximate f⁻¹(y) by finding x where f(x)=y using bisection search.
Linear Equation SolverSolve ax + b = 0 for x, showing the solution and verification step.
Logarithm CalculatorCompute logarithms in any base, plus natural log and antilog.
Matrix CalculatorAdd, multiply, transpose and invert matrices, and find determinants.
Number Sequence CalculatorFind terms and sums of arithmetic, geometric and Fibonacci sequences.
Piecewise Function CalculatorEvaluate a piecewise-defined function at x by selecting the matching interval branch.
Polynomial DivisionDivide one polynomial by another using synthetic or long division, showing quotient and remainder.
Polynomial ExpansionExpand (ax+b)^n using the binomial theorem, showing each term and coefficient.
Polynomial FactorizationFactor a polynomial into linear factors over the rationals using the rational root theorem.
Polynomial RootsFind all real and complex roots of a polynomial up to degree 4 using exact algebraic methods.
Polynomial SolverFind rational roots of a polynomial up to degree 6 using the rational root theorem.
Quadratic Formula CalculatorSolve any quadratic equation with real or complex roots, vertex and discriminant.
Quartic Equation SolverSolve ax⁴+bx³+cx²+dx+e=0 for all four roots via Ferrari's resolvent-cubic method.
Radical SimplifierSimplify √n by extracting the largest perfect-square factor: √n = a√b.
Range CalculatorEstimate the range of f(x) by evaluating it across its domain and reporting observed min/max.
Ratio CalculatorSimplify ratios, solve proportions and scale ratios up or down.
Rational Expression SimplifierAdd, subtract, multiply or divide two rational expressions (fractions of polynomials).
Root CalculatorFind square roots, cube roots and any nth root of a number.
Simultaneous Equation SolverSolve a system of two linear equations in two unknowns using Cramer's rule.
Slope CalculatorFind the slope, angle and line equation through two points.
Trigonometry CalculatorEvaluate all six trig functions and their inverses in degrees or radians.