Factor expressions
Factor a quadratic like x² + 5x + 6 quickly
Random trial-and-error for the two numbers wastes time; a sum-and-product search is systematic.
Spot it when
You need to factor x² + bx + c (or split the middle term of ax² + bx + c).
Watch it solved
Vyaṣṭisamaṣṭhi balances the "individual" (the parts) with the "whole." For x² + bx + c, we need two parts that fit both the product and the sum.
Factor the trinomial
Vyaṣṭisamaṣṭhi balances the "individual" (the parts) with the "whole." For x² + bx + c, we need two parts that fit both the product and the sum.
⚡ Speed Advantage
See how few steps Vedic method needs!
When you’ll actually hit this
Real moments — exams, homework, competitions — where this shortcut earns its keep.
A garden of area x² + 5x + 6 needs its two side lengths for the next part of the question.
Two numbers with product 6 and sum 5 are 2 and 3 → (x+2)(x+3).
A non-monic quadratic 6x² + 5x − 6 appears and you need its factors fast.
Split the middle term using the sum/product targets → (2x+3)(3x−2).
A sign-trap quadratic in class: product negative, sum positive.
Product −21, sum 4 → 7 and −3 → (x+7)(x−3).
The method behind it
व्यष्टिसमष्टि
Vyaṣṭisamaṣṭhi
“Part and whole”
Factor a quadratic by finding two numbers whose sum is the middle coefficient and product is the last — the Vedic way to factor trinomials.
trial and error factoring — variable steps.
systematic sum-and-product recognition.
Use when
- • Quadratic trinomials, factorization problems
Avoid when
- • Irreducible polynomials over integers