Question

A rectangle with an area of x2 – 4x – 12 square units is represented by the model.

An algebra tile configuration. In the Product spot are 21 tiles in 3 rows. 1 tile is labeled + x squared. In the same row are 6 tiles labeled negative 6. Below + x squared are 2 tiles labeled + x, and to the right of the + x tiles are 12 tiles labeled negative.
What side lengths should be used to model the rectangle?

(x + 2) and (x – 6)
(x + 6) and (x – 2)
(x + 2) and (x – 10)
(x + 10) and (x – 2)

Answer 1

(x + 2) and (x − 6)

Reason: x^2 − 4x − 12 factors as (x + 2)(x − 6) because 2 · (−6) = −12 and 2 + (−6) = −4. This matches the tile model: one side gives +2 unit tiles and the other gives −6 unit tiles.