Generic Rectangle Calculator

Use a generic rectangle to expand or factor a quadratic.

Factor root 1 -2
Factor root 2 -5

Formula: Find roots so a(x − r₁)(x − r₂) = ax² + bx + c

Step-by-step with your numbers:
1. Values used:
2. a = 1
3. b = 7
4. c = 10
5.
6. Factor root 1 = -2
7. Factor root 2 = -5
Did we solve your problem today?

The generic rectangle (area model) helps factor a quadratic by splitting the middle term.

The math behind it

The diagonal cells of the rectangle hold ax² and c; the other diagonal must multiply to ac and add to b. The roots give the factors a(x − r₁)(x − r₂).

Worked example

x² + 7x + 10 → roots −2 and −5 → (x + 2)(x + 5).

FAQ

When can't I factor over integers?

When the discriminant b² − 4ac isn't a perfect square.