Polynomial long division
AskSia walks through long division of polynomials step-by-step, with each subtraction and bring-down shown clearly. Useful when the divisor is degree 2 or higher and synthetic division does not apply.
Long division
AI Solver by AskSia
Remainder Solver: long division, synthetic, or theorem
AskSia finds the remainder of any integer or polynomial division step-by-step. Choose long division, synthetic division, or the remainder theorem, or let AskSia pick the cleanest method. Quotient and remainder are both shown, with a divisibility test where appropriate.
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
98% · Verified
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 remainder solver?
The AskSia remainder solver is an AI tool that finds the remainder of any division problem, integer or polynomial. For integer division, AskSia shows the standard long division and identifies the remainder. For polynomial division, AskSia walks through long division step-by-step, applies synthetic division when the divisor is of the form (x minus c), or uses the remainder theorem (the remainder of p(x) divided by (x minus c) is just p(c)). The quotient, remainder, and a divisibility check appear on every solve.
98%
solution accuracy
50M+
problems solved
~1.5s
avg solve time
A+
study-ready explanations
Why AskSia Solver
Three methods for remainders, picked for the problem.
Long division works for any divisor. Synthetic division is faster for (x minus c) divisors. The remainder theorem is fastest when you only need the remainder, not the quotient. AskSia picks the right tool.
Synthetic division for linear divisors
When the divisor is (x minus c), AskSia uses synthetic division, which is faster and easier to check. The synthetic division layout is shown with every coefficient labeled.
Synthetic, fast
Remainder theorem when only the remainder matters
If the problem asks only for the remainder (not the quotient) and the divisor is (x minus c), AskSia computes p(c) directly via the remainder theorem. This is the fastest method and works on AP and SAT problems.
Remainder theorem
Factor theorem flag
When the remainder is zero, the divisor is a factor of the dividend. AskSia flags this explicitly, useful for problems asking whether (x minus c) is a factor of a polynomial.
Factor check
Integer remainders too
For Pre-Algebra and middle school problems, AskSia handles integer division with the standard long division layout. The quotient and remainder are both shown, with a check by multiplication.
Integer division
Modular arithmetic
AskSia handles modular arithmetic notation (a mod n) for problems in number theory, discrete math, and intro CS. The result is shown in the range 0 to n minus 1.
Modular notation
How It Works
Three taps to a found remainder.
Step 01
Capture the division
Snap a photo, paste, or type the division: integer division (like 47 ÷ 6) or polynomial division (like x³ + 2x² - x - 2 divided by x minus 1). AskSia reads both formats.
Input mode
Snap a Photo
Textbook, handwriting, screenshot
Paste Text
Word problem or equation
Calculator
LaTeX-ready equation editor
Step 02
Pick the method, or let Sia pick
AskSia picks long division for general polynomial divisors, synthetic for (x minus c) divisors, the remainder theorem when only the remainder is needed, or standard long division for integers.
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 quotient and remainder
Both the quotient and the remainder are shown clearly. If the remainder is zero, AskSia flags the divisor as a factor. Generate practice problems or ask follow-up questions.
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
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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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98%
1.4s
Area between y=2x & y=x²
A = 4/3 sq. units ✓
Use Cases
Every remainder problem, every level.
Pre-Algebra integer remainders
Standard integer long division with the quotient and remainder both labeled. AskSia shows the long division grid clearly and verifies by multiplication.
Pre-Algebra
Algebra 2 polynomial division
Polynomial long division and synthetic division as taught in Algebra 2 and College Algebra. AskSia walks through each subtraction, with the layout matching textbook conventions.
Algebra 2
Remainder theorem on AP and SAT
AP and SAT problems often ask for the remainder when p(x) is divided by (x minus c), without needing the quotient. AskSia uses the remainder theorem to compute p(c) directly, the fastest method.
AP, SAT
Factor theorem and root testing
To check whether (x minus c) is a factor of p(x), evaluate p(c). If the result is zero, it's a factor. AskSia confirms factorhood explicitly, useful for setup before polynomial factoring.
Factor theorem
Modular arithmetic
Number theory and intro CS problems involving 'a mod n' notation. AskSia handles modular reduction and explains the remainder in the standard 0 to n-1 range.
Modular arithmetic
Word problems with remainders
Pre-Algebra word problems about distributing items (with some left over), repeating patterns, and calendar arithmetic. AskSia translates the prose into the right division and interprets the remainder in context.
Word problems
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 a polynomial remainder?
AskSia picks the cleanest method based on the divisor. For divisors of the form (x minus c), the remainder theorem applies: the remainder of p(x) divided by (x minus c) is just p(c), no division needed. For other linear divisors, synthetic division is fast. For divisors of degree 2 or higher, long division is the right choice. AskSia walks through whichever method applies step-by-step, with each subtraction, bring-down, and final remainder labeled clearly.
What is the remainder theorem and when does AskSia use it?
The remainder theorem says that when a polynomial p(x) is divided by (x minus c), the remainder is p(c), the value of the polynomial evaluated at c. This is much faster than long or synthetic division when you only need the remainder. AskSia uses the remainder theorem automatically when the divisor is of the form (x minus c) and the problem asks only for the remainder (not the quotient). It's especially useful on AP and SAT problems where the remainder is the only requested value.
How is the remainder theorem related to the factor theorem?
The factor theorem is a corollary of the remainder theorem: (x minus c) is a factor of p(x) if and only if p(c) = 0 (the remainder is zero). So to check whether (x minus c) is a factor, just evaluate p(c). If it's zero, it's a factor and c is a root. If it's nonzero, it's not a factor. AskSia uses this to test candidate factors for polynomials, especially in problems asking 'is (x minus c) a factor of p(x)?'
Can AskSia find integer remainders with modular notation?
Yes. For 'a mod n' notation (common in number theory, discrete math, and intro CS), AskSia computes a divided by n and returns the remainder in the standard range 0 to n minus 1. For negative integers, AskSia uses the mathematical convention (always non-negative result), not the programming-language convention (which can return negative results in some languages). The work is shown so you can verify the modular reduction by hand.
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.
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Any division. Quotient and remainder, done.
Join 2M+ students using AskSia to find remainders of polynomial and integer division, with long division, synthetic, or the remainder theorem picked for each problem.
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