How this calculator works
Two factors A and B determine their sum and product immediately. If only the sum and product are known, each factor is a root of the same quadratic. A negative discriminant means no real pair exists. A zero known factor and zero product do not uniquely determine the other factor, so that recovery mode requires a non-zero factor.
Formula
S = A + B; P = AB; A and B solve t^2 - St + P = 0.
Worked example
With sum 7 and product 12, solve t^2 - 7t + 12 = 0. The factors are 3 and 4 because 3 + 4 = 7 and 3 x 4 = 12.
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Frequently asked questions
Can a factor be negative?
Yes. A negative product requires opposite signs; a positive product permits two positive or two negative factors.
Why can the factors swap places?
Addition and multiplication are commutative. Sum-product mode lists the smaller factor first.
How does this help factor a trinomial?
For x^2 + bx + c, a pair with sum b and product c gives (x + A)(x + B).