Question

Complete the statements to explain how to factor x2 + x – 12 using algebra tiles.

Represent the trinomial using 1 positive x2-tile,
, and
.



Form a rectangle with the tiles, adding zero pairs as needed. How many zero pairs are needed?



Drag tiles onto the board to represent each factor. What is the factorization? x2 + x – 12 =

Answer 1

Represent the trinomial using 1 positive x^2-tile, 1 positive x-tile, and 12 negative 1-tiles.

To form a rectangle you must add 4 zero pairs (four +1 tiles and four −1 tiles).

Arranging the tiles gives side lengths x + 4 and x − 3, so
x^2 + x − 12 = (x + 4)(x − 3).