Factoring tried first
AskSia tries common-factor extraction, grouping, difference of squares, sum or difference of cubes, and perfect-square patterns before going further. Cleanest factoring is shown when it exists.
Factoring first
AI Solver by AskSia
Polynomial Equation Solver: every root, every degree
Type or photograph any polynomial equation. AskSia factors, applies the rational root theorem, uses synthetic division, or solves numerically when needed, then returns all real and complex roots with multiplicities and a labeled graph.
Works with word problems, equations, code, and science prompts.
∫ 3x² · sin(x) dx
SubjectsCalculusAlgebraPhysicsChemistryBiologyCSStatisticsEcon
4.9 / 5 · trusted by 2M+ students · 50M+ problems solved
asksia.ai/solver
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Problem
Find the area enclosed between y = x² and y = 2x in the first quadrant.
1
Find the points of intersection
Set the curves equal: x² = 2x → x(x - 2) = 0, so x = 0 and x = 2.
2
Identify which curve is on top
On (0, 2), 2x > x², so y = 2x is the upper curve.
3
Set up the area integral
A = ∫₀² (2x - x²) dx
4
Integrate term-by-term
A = [ x² - x³/3 ]₀²
Final Answer
A = 4/3 sq. units
Quick Answer
What is the AskSia Polynomial Equation Solver?
AskSia's Polynomial Equation Solver is an AI tool that solves polynomial equations of any degree a high school or college math student is likely to see. AskSia tries factoring first, then the rational root theorem with synthetic division, then the quadratic formula on remaining quadratic factors, and finally numeric methods for higher-degree polynomials with no rational roots. Returns all real and complex roots with multiplicities and verifies each root by substitution.
98%
solution accuracy
50M+
problems solved
~1.5s
avg solve time
A+
study-ready explanations
Why AskSia Solver
Every polynomial, every root.
Degree 2 through 6 and beyond. Factoring, rational root, synthetic division, and the quadratic formula on the remaining quadratic factor. AskSia picks the path and shows the work.
Rational root theorem
For polynomials without obvious factoring, AskSia lists all possible rational roots from p over q, tests them by substitution or synthetic division, and reduces the degree step by step.
Rational root
Synthetic division shown
Every rational root found is divided out by synthetic division with the coefficients lined up cleanly. The quotient polynomial is what comes next in the work.
Synthetic division
Complex roots from the quadratic
When the polynomial reduces to a quadratic with negative discriminant, AskSia applies the quadratic formula and writes the complex conjugate pair.
Complex roots
All roots, with multiplicities
AskSia reports every root and its multiplicity, so a degree-5 polynomial returns 5 roots (counted with multiplicity), as the fundamental theorem of algebra requires.
Multiplicities
Labeled graph
Auto-generated graph of the polynomial with real roots marked on the x-axis and turning points labeled. Complex roots are noted separately. The visual confirms degree, end behavior, and number of real roots.
Graph included
How It Works
Three taps to all roots.
Step 01
Capture the polynomial
Snap a photo, paste the polynomial, or type with LaTeX. Coefficients can be entered as fractions, decimals, or symbolic.
Input mode
Snap a Photo
Textbook, handwriting, screenshot
Paste Text
Word problem or equation
Calculator
LaTeX-ready equation editor
Step 02
Watch Sia factor and divide
Factoring tried first, then rational root theorem with synthetic division shown, then the quadratic formula on the remaining factor. Each step has a plain-English reason.
1
Set curves equal
x² = 2x → x = 0, x = 2
2
Set up the integral
A = ∫₀² (2x - x²) dx
3
Evaluate
A = [x² - x³/3]₀² = 4/3
Step 03
See all roots and check
Every root listed with multiplicity, complex roots written as conjugate pairs, and substitution check on each. Graph appears with real roots labeled.
Auto-generated diagram
Region between y = 2x and y = x² — area = 4/3
Available On
Solve anywhere
you study.
Every solve syncs across Web, iOS, and Android — start it at your desk, finish on your phone.
Web App
Full study studio
Split-panel interface with the worked solution on the left, the auto-generated diagram and AI tutor chat on the right.
Drag & drop image upload + LaTeX equation editor
Auto-generated diagrams render alongside steps
Side-panel AI tutor chat for hints and alt methods
Export to PDF, DOCX, Notion, or Google Docs
Hi! What are we studying today?
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Calculus
98% verified
1.4s
Step 4 of 4 · Evaluate
A = [x² - x³/3]₀² = 4/3
Mobile App
Snap & solve, anywhere
Open the camera, frame the problem, and the worked solution plus diagram appear in seconds.
One-tap snap-and-solve on iOS and Android
Pinch-to-zoom diagrams, swipe between steps
Auto-sync solves with your Web library
Offline review of saved solutions and flashcards
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Calc
98%
1.4s
Area between y=2x & y=x²
A = 4/3 sq. units ✓
Use Cases
Every polynomial, every degree.
Cubic equations
Cubic polynomials in Algebra 2 and Pre-Calc. AskSia tries factoring by grouping or a known root from the rational root theorem, then solves the remaining quadratic.
Cubic
Quartic and higher polynomials
Degree-4 and higher polynomials by rational root and repeated synthetic division. Numeric methods are used when no rational root exists.
Quartic plus
Polynomials with complex roots
Polynomials whose roots are not all real. AskSia returns conjugate pairs and writes the full factorization over the complex numbers.
Complex roots
Pre-Calc and College Algebra exam prep
After any solve, generate similar polynomial problems at the right difficulty for your class, test, or AP exam.
Exam prep
Polynomial factorization
When the question asks to factor rather than solve, AskSia returns the complete factorization over the reals or over the complex numbers depending on what is asked.
Factorization
Check your roots
Paste your candidate roots and AskSia substitutes them back into the polynomial to flag any that fail.
Root check
Compare
AskSia vs. ChatGPT,
Photomath & Symbolab.
General chatbots hallucinate. Photo solvers stop at math. AskSia is built for actual coursework with verified accuracy, visual learning, and every subject.
| Feature | AskSia Solver | ChatGPT | Photo Solvers |
|---|---|---|---|
| Solution accuracy | ✓ 98% | ~70-85%, hallucinations | ~90%, math only |
| Auto-generated diagrams | ✓ Every solve | Inconsistent / broken | Graphs only, math-only |
| Step-by-step explanations | ✓ Numbered + plain English | Inconsistent depth | ✓ Math steps |
| Subject coverage | ✓ Math, Physics, Chem, Bio, CS, Econ | ✓ Wide but unverified | Math only |
| Photo input | ✓ Handwriting + diagrams + code | Photos OK, weak on handwriting | ✓ Math photos only |
| Answer verification | ✓ Self-checked before display | No verification | Math engine only |
| Tutor follow-ups | ✓ Hints, alt methods, ELI5 | ✓ General chat | Not available |
| Practice and flashcards | ✓ One-tap from any solve | Manual prompting | Not available |
| Code debugging | ✓ Python, Java, C++, SQL... | ✓ Yes | Not available |
| Free to start | ✓ Daily solves, no card | Limited model access | Steps locked behind paywall |
FAQ
Frequently asked questions.
How does AskSia find polynomial roots?
First, AskSia tries factoring (common factor, grouping, difference of squares, sum or difference of cubes). If factoring does not finish the job, AskSia applies the rational root theorem to list candidate rational roots, tests them by synthetic division, and reduces the degree each time a root is found. When the polynomial reduces to a quadratic, AskSia applies the quadratic formula for the remaining two roots. For polynomials with no rational roots and degree 5 or higher, AskSia uses numeric methods to approximate the real and complex roots.
Does AskSia return complex roots?
Yes. By the fundamental theorem of algebra, a polynomial of degree n has exactly n roots counting multiplicity. AskSia reports all of them. When complex roots appear, they come in conjugate pairs (for polynomials with real coefficients) and AskSia writes them as a + bi and a minus bi.
Can AskSia show synthetic division clearly?
Yes. Synthetic division is shown with the coefficients lined up, the root in the corner, the bring-down step, and the multiply-add work. The quotient polynomial after each division is written explicitly so you can follow degree reduction step by step.
Can AskSia factor as well as solve?
Yes. When the prompt asks to factor a polynomial rather than solve it, AskSia returns the complete factorization. Over the real numbers, irreducible quadratic factors are left in place. Over the complex numbers, every factor is linear. You can ask for either.
How accurate is AskSia?
AskSia is engineered for accuracy on standard high school and college coursework. Accuracy comes from subject-specialized models, a symbolic verification pass that catches arithmetic errors, and a self-check step that re-derives the answer before showing it to you.
Can I get practice problems and flashcards?
Yes. After any solve, ask Sia to generate similar practice problems at SAT, ACT, AP, IB, or college difficulty, or build a flashcard set on the underlying concept in one tap. Useful for exam prep and spaced repetition before a quiz, midterm, or final.
How much does AskSia cost?
AskSia has a free plan that includes daily solves across all subjects. AskSia Pro and Super include unlimited solves, advanced subjects, the full AI tutor companion, exports, and priority response speed. See pricing for details.
Start Today
Every polynomial, every root, worked out.
Join 2M+ students using AskSia to find all real and complex roots of polynomial equations from degree 2 through 6 and beyond, with factoring, the rational root theorem, synthetic division, and a labeled graph on every solve.
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