How this calculator works
The box method splits bx into two terms whose coefficients add to b and multiply to ac. Place ax^2 and c in opposite cells, then place the split terms in the other two cells. Grouping the rows and columns gives the same factors as solving the quadratic. A negative discriminant prevents a real split.
Formula
D = b^2 - 4ac; t1 = (b - sqrt(D))/2, t2 = (b + sqrt(D))/2; t1 + t2 = b and t1*t2 = ac.
Worked example
For 2x^2 + 7x + 3, ac = 6. Split 7x as x + 6x. The cells are 2x^2, x; 6x, 3, so the factors are (2x + 1)(x + 3).
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Frequently asked questions
Must the factors be integers?
No. Real decimal coefficients are accepted. Non-integer roots and factors are displayed approximately.
What if the discriminant is negative?
There is no factorization into real linear factors. The result states this instead of inventing a real box split.
Can the two factors be equal?
Yes. A zero discriminant gives a repeated root and two equal linear factors, apart from the leading multiplier.