How this calculator works
Find the real zeros with the quadratic formula, then write a(x - r1)(x - r2). This approach includes irrational factors and repeated roots. A negative discriminant means the quadratic cannot be split into real linear factors. The leading coefficient must be non-zero.
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 x^2 - 5x + 6, the zeros are 2 and 3. Therefore x^2 - 5x + 6 = (x - 2)(x - 3). Expanding produces x^2 - 3x - 2x + 6.
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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.