AC method, fully shown.
The search for two integers that multiply to a*c and add to b is laid out as a small table you can scan.
AC method
AI Solver by AskSia
Quadratic Factoring Solver: AC method, grouping, more
Type the quadratic or photograph it. AskSia checks the discriminant first, extracts any common factor, then uses the AC method or grouping to find the factored form. Special products like x^2-9 and x^2+6x+9 get recognized and labeled. When factoring over the rationals is impossible, AskSia says so and offers the quadratic formula.
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
How do you factor a quadratic?
To factor ax^2+bx+c, first pull out the GCF if there is one. For monic quadratics (a=1), find two integers that multiply to c and add to b. For non-monic, use the AC method: find two integers that multiply to a*c and add to b, split the middle term, then factor by grouping. Check by expanding. If the discriminant b^2-4ac is not a perfect square, the quadratic does not factor over the rationals and you should solve it with the quadratic formula instead.
98%
solution accuracy
50M+
problems solved
~1.5s
avg solve time
A+
study-ready explanations
Why AskSia Solver
Why students use AskSia to factor quadratics.
Every method shown, every irreducible case flagged.
Grouping made visible.
After the middle term splits, the four-term polynomial gets grouped, GCFs come out of each pair, and the common binomial factor falls out.
Grouping
Special products recognized.
Difference of squares, perfect square trinomials, and sum/difference of cubes get labeled before you start hunting.
Patterns
Discriminant check first.
If b^2-4ac is not a perfect square, AskSia flags that the quadratic does not factor over the rationals, saving you the search.
Smart
Expansion verification.
AskSia expands the factored form and confirms it equals the original quadratic before showing you the answer.
Verified
Graph included.
The parabola appears with x-intercepts marked at the zeros of each factor, giving you a visual check.
Visual
How It Works
Factor a quadratic in three steps.
Step 01
Enter the quadratic.
Type, paste, photograph, or speak ax^2+bx+c. AskSia parses the coefficients and runs the discriminant check.
Input mode
Snap a Photo
Textbook, handwriting, screenshot
Paste Text
Word problem or equation
Calculator
LaTeX-ready equation editor
Step 02
AskSia picks the method.
Monic uses simple integer-pair search. Non-monic uses the AC method with grouping. Special products get labeled and shortcut applied.
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
Read the factored form.
Final factored form is shown, expanded to verify, and the parabola is plotted with intercepts at each zero.
Auto-generated diagram
Region between y = 2x and y = x² — area = 4/3
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Every solve syncs across Web, iOS, and Android — start it at your desk, finish on your phone.
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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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Calc
98%
1.4s
Area between y=2x & y=x²
A = 4/3 sq. units ✓
Use Cases
What quadratic factoring covers.
Monic quadratics.
x^2+5x+6, x^2-x-12, and similar. AskSia finds the integer pair and writes (x+m)(x+n).
Algebra 1
Non-monic quadratics.
2x^2+7x+3 and similar. AskSia walks through the AC method and grouping.
Algebra 2
Difference of squares.
x^2-49, 4x^2-25, and harder versions like 9x^2-16y^2. Pattern recognized, factored, labeled.
Pattern
Perfect square trinomials.
x^2+10x+25 and similar. AskSia checks (b/2)^2 = c and writes (x+b/2)^2.
Pattern
Irreducible cases.
When the discriminant is not a perfect square, AskSia says so and offers the quadratic formula instead.
Edge cases
Solving by factoring.
Set each factor to zero, read off the solutions, and verify by substituting back into the original.
Solve
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.
What if the quadratic does not factor?
AskSia checks the discriminant b^2-4ac first. If it is not a perfect square, the quadratic is irreducible over the rationals and AskSia tells you so directly, then offers to solve it by the quadratic formula or by completing the square instead of pretending a factoring exists.
How does the AC method work?
For ax^2+bx+c, find two integers that multiply to a*c and add to b. Use them to split the middle term, then factor by grouping. AskSia shows the integer search as a small table, then performs the split and grouping with every step labeled, so you can apply the same method by hand.
Can AskSia factor over the complex numbers?
Yes. If you want complex factorization, AskSia uses the quadratic formula to find the (complex) roots and writes the quadratic as a*(x-r1)*(x-r2) with the conjugate-pair structure made explicit. The default is rational factoring; you toggle to complex when needed.
What about quadratics with two variables, like in conic sections?
AskSia handles quadratics in x and y. For factoring x^2-y^2 or 4x^2-9y^2 the difference-of-squares pattern still applies. For mixed quadratics like x^2+5xy+6y^2, the AC method extends naturally by treating y as a coefficient, and AskSia shows the resulting (x+2y)(x+3y) factorization with the same logic.
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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Factor any quadratic. Or learn why it cannot factor.
Join 2M+ students using AskSia to factor quadratics with full transparency. AC method, grouping, special products, discriminant check, photo input, and a graph on every result.
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