Check your answers
Confirm a factorization is correct without expanding it
Multiplying the factors back out to check wastes time — one substitution disproves a wrong answer.
Spot it when
You factored a polynomial and want to be sure before using it.
Watch it solved
Guṇakasamuccayaḥ: "the product of the sums equals the sum of the products." A true factorization is an identity — so it must hold for ANY value of x.
Did we factor correctly?
Guṇakasamuccayaḥ: "the product of the sums equals the sum of the products." A true factorization is an identity — so it must hold for ANY value of x.
⚡ 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.
You claim (x+2)(x+3) factors x² + 5x + 6 and want a fast confidence check.
Test x = 1: factor side = 12, polynomial side = 12 — they agree.
A multi-mark question depends on an earlier factorization being correct.
Plug in x = 0 and x = 1; both sides match → safe to build on it.
A quick coefficient-sum check in class to catch a wrong split.
Sum of coefficients of the factors, multiplied, must equal that of the product (both at x = 1).
The method behind it
गुणकसमुच्चयः
Guṇakasamuccayaḥ
“The factors of the sum is the sum of the factors”
The factors of an expression when evaluated at a value equal the expression's value — use this to verify factorizations.
multiply out factors and compare — many steps.
evaluate at a test point — 1 step per factor.
Use when
- • After factoring a polynomial — verify the result
Avoid when
- • Primary computation