Diamond Problem Calculator
With our diamond problem calculator you'll solve any type of diamond problem.
Factored form(x + 3)(x + 4)factors over the integers
Roots-3 and -4
Diamond numbers3 and 4they add to 7 and multiply to 12
a × c12
Discriminant1
Perfect square trinomial?Noa zero discriminant means (x − r)²
Check by expanding
| Original | x^2 + 7x + 12 |
| Factored | (x + 3)(x + 4) |
| Expanded back | x^2 + 7x + 12 |
The method
find p and q with p + q = b and pq = ac
The diamond method
To factor ax² + bx + c, look for two numbers that multiply to ac and add to b. Those numbers split the middle term so the expression groups into two factors.
For x² + 7x + 12: ac is 12 and b is 7, so 3 and 4 work — giving (x + 3)(x + 4). When no integer pair exists, the trinomial does not factor over the integers, and the roots above will be irrational.