Math

Generic Rectangle Calculator

Use a generic rectangle to expand or factor a quadratic.

Parameters Live Compute
Calculated Output
Factor root 1 -2
Factor root 2 -5
Formula: Find roots so a(x − r₁)(x − r₂) = ax² + bx + c
Step-by-Step Breakdown
1. Values used:
2. a = 1
3. b = 7
4. c = 10
5.
6. Factor root 1 = -2
7. Factor root 2 = -5
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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).

Frequently Asked Questions

When can't I factor over integers?

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

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