Question

The partial factorization of x2 – x – 12 is modeled with algebra tiles.

An algebra tile configuration. 4 tiles are in the Factor 1 spot: 1 is labeled + x, 3 are labeled +. 1 tile is in the Factor 2 spot and is labeled + x. 20 tiles are in the Product spot: 1 is labeled + x squared, 3 are labeled + x, the 4 tiles below + x squared are labeled negative x, and the 12 tiles below the + x tiles are labeled negative.
Which unit tiles are needed to complete the factorization?

3 negative unit tiles
3 positive unit tiles
4 negative unit tiles
4 positive unit tiles

Answer 1

4 negative unit tiles.

Reason: x^2 − x − 12 factors as (x + 3)(x − 4), so the second factor needs four negative unit tiles (−4).