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Utilnivo

Algebra Calculator

Equations, matrices, and complex numbers together — exact when verified, approximate when not.

  • 100% Free
  • No signup
  • Private & secure
  • Instant results
  • On your device

Private on your device

Your information stays on your device and is not uploaded.

Related tools

Use one algebra workspace for polynomial equations (exact rational roots through degree 4 when verified), matrix arithmetic with copyable results, and complex rectangular/polar/exponential conversions. Standalone equation, matrix, and complex tools remain available for focused workflows.

Utilnivo’s Algebra Calculator is a unified workspace for equations, matrices, and complex numbers. It is designed for students and technical users who switch among these tasks in one session without uploading data.

For single-variable polynomials with rational coefficients of degree four or less, the solver extracts coefficients from the parsed expression tree, lists rational-root candidates, and accepts a root only after exact re-substitution succeeds. Deflation preserves multiplicity. Remaining linear and quadratic factors are solved exactly when the discriminant is a perfect square in lowest terms.

When exact verified solving is unavailable—irrational roots, complex roots, higher degree, or non-polynomial input—the tool falls back to numerical search, labels results Approximate, and shows the configured display precision. Show steps lists the operations that actually ran, never generic filler prose.

The matrix panel provides a spreadsheet-style grid for A and B with common operations and copyable scalar or matrix result cards. The complex panel keeps rectangular a+bi, polar magnitude and degrees, exponential form, and the conjugate in sync. Everything runs locally in your browser; saved sessions stay on this device.

Keep the dedicated Equation Solver, Matrix Calculator, and Complex Number Calculator routes for focused workflows. Use this algebra workspace when you want all three surfaces together with shared precision and session state.

How to use this tool

Enter an equation such as x^3-6x^2+11x-6=0 and press Solve. Edit Matrix A and B in the grid, then choose an operation. Type a complex number like 3+4i or edit a, b, r, and θ directly. Save a session on this device to restore the full workspace later.

Worked example

Solving x^3-6x^2+11x-6=0 yields exact roots x=1, 2, and 3 after rational-root checks and verified deflation. For the sample upper-triangular Matrix A, det(A)=1. Converting 3+4i shows magnitude 5 and argument about 53.13°.

When to use this

  • Homework that mixes polynomials, matrices, and complex forms in one session.
  • Checking exact rational roots before trusting a numerical estimate.
  • Converting a+bi to polar degrees without leaving the algebra workspace.

Common examples

  • x^3-6x^2+11x-6=0
  • x^2-5x+6=0
  • matrix determinant and inverse
  • 3+4i polar form

Common mistakes

  • Treating Approximate roots as Exact closed forms.
  • Expecting every cubic or quartic to have an exact rational factorization.
  • Editing polar magnitude to a negative value.

How it works

The Algebra Calculator combines equation solving, matrix operations, and complex-number conversion in one on-device workspace. Polynomials with rational coefficients up to degree 4 can be solved exactly when every root verifies by re-substitution; otherwise a numerical search reports Approximate results with method notes. Matrices support add, subtract, multiply, determinant, inverse, transpose, rank, trace, and RREF. Complex values sync across rectangular, polar (degrees), and exponential forms.

Limitations

Results are based on the inputs you provide and may not cover every edge case. This tool is for general use and is not professional advice.

Privacy and file handling

Your data stays on your device and is not uploaded.

Formula or method

Exact solving walks the expression AST to extract rational coefficients, applies the rational-root theorem, verifies each candidate by exact substitution, deflates, and finishes remaining linear or quadratic factors. Unsupported cases fall back to numerical root finding. Matrix ops use the shared linear-algebra kernel. Complex conversions use rectangular ↔ polar transforms with θ in degrees.

FAQ

Frequently asked questions

When are roots labeled Exact?

Only when the expression is a supported single-variable polynomial with rational coefficients of degree 4 or less and every root passes exact re-substitution after factorization. Otherwise results are Approximate.

Does this replace the Equation Solver and Matrix Calculator?

No. Those dedicated tools stay live for focused work. This page combines them when you want one session across equations, matrices, and complex numbers.

Is my algebra work uploaded?

No. Solving, matrix ops, and complex conversions run locally. Saved sessions stay on this device.

Related pages

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