How does AskSia find all factors of a number?
AskSia first finds the prime factorization of the number using trial division (testing primes 2, 3, 5, 7, ... in order). For example, 60 = 2² × 3 × 5. Then AskSia constructs all positive factors by combining the primes in every possible way: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. The total number of factors is (2 + 1)(1 + 1)(1 + 1) = 12. AskSia lists all factors in ascending order and shows the prime factorization explicitly, which is useful for related tasks like finding GCF, LCM, and counting divisors.
What's the order of operations for polynomial factoring?
Always start with the greatest common factor (GCF) of all terms, pulling it out front. After GCF, check the structure: two terms with subtraction often means difference of squares (a² minus b²) or difference of cubes (a³ minus b³); two terms with addition often means sum of cubes (a³ + b³). Three terms (a trinomial) factors with the AC method or simple trinomial factoring. Four terms usually factor by grouping. For higher-degree polynomials (cubic and up), use the rational root theorem to find one root, factor out (x minus root) via synthetic division, and repeat on the quotient. AskSia walks through this hierarchy automatically.
What is the AC method for trinomial factoring?
The AC method factors trinomials of the form ax² + bx + c when the leading coefficient a is not 1. The steps: (1) compute ac (the product of leading coefficient and constant); (2) find two numbers that multiply to ac and add to b; (3) use those two numbers to split the middle term bx into two terms; (4) factor by grouping the four resulting terms. For example, 6x² + 7x + 2: ac = 12, two numbers that multiply to 12 and add to 7 are 3 and 4. Split: 6x² + 3x + 4x + 2. Group: 3x(2x + 1) + 2(2x + 1) = (3x + 2)(2x + 1).
When is a polynomial irreducible?
A polynomial is irreducible over the rationals if it cannot be factored into lower-degree polynomials with rational coefficients. Quadratics with negative discriminant (no real roots) are irreducible over the rationals (their roots are complex conjugates). Some higher-degree polynomials with no rational roots are also irreducible over the rationals, even though they can be factored over the reals or complex numbers using Cardano's formula or numerical methods. AskSia identifies irreducible factors and notes when no further factoring is possible over the rationals.
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.