Final answer:
The correct factorization of the expression x^2 - x - 2 is (x - 2)(x + 1), which corresponds to the algebra tile configuration with three tiles in Factor 1 and two tiles in Factor 2, ultimately resulting in the correct products.
Step-by-step explanation:
To factorize the quadratic expression x2 - x - 2, we are looking for two binomials that multiply together to give us the original expression. Given that when two positive numbers are multiplied, the result is positive, and when two negative numbers are multiplied, the result is also positive, we realize that to obtain the middle term -x and the constant term -2, one of the binomials will have a negative term while the other will have a positive term.
After testing possible factors, we see that (x - 2)(x + 1) will result in x2 + x - 2x - 2, which simplifies to x2 - x - 2. Therefore, correct factorization matches the algebra tiles configuration where the Factor 1 has 1 labeled +x, 1 labeled +, and 1 labeled -, and Factor 2 has 1 labeled +x and 1 labeled -. This configuration will produce the appropriate Product spot with tiles labeled accordingly to the expanded expression.