Final answer:
The factorization of the given quadratic expression requires 4 positive unit tiles to complete the model using algebra tiles. These tiles correspond to the positive integer in one of the binomials that make up the factorization of the expression.
Step-by-step explanation:
The question involves the factorization of a quadratic expression using algebra tiles. Factorization is the process of expressing an algebraic expression as the product of its factors. Given the expression x2 - x - 12, we are seeking to factor it into two binomials of the form (x+a)(x+b), where a and b are integers that satisfy ab = -12 (the constant term) and a+b = -1 (the coefficient of the linear term x).
Considering the multiplication rules for sign: when two positive numbers multiply, the result is positive; when two negative numbers multiply, the result is also positive; and when a positive number multiplies with a negative number, the result is negative. Therefore, for our expression, we need two numbers that multiply to -12 and add up to -1. The numbers that satisfy these conditions are 4 and -3. Hence, the quadratic factors into (x+4)(x-3).
To match the model with algebra tiles, we need to add 4 positive unit tiles to complete the factorization corresponding to the positive unit tiles required for the term +4 in one of the binomials. Therefore, the correct answer is c) 4 positive unit tiles.