To factorize the quadratic equation [tex]\(x^2 - x - 12\)[/tex], we need to find two numbers that multiply to give the constant term (-12) and add up to give the coefficient of the linear term (-1). The numbers satisfying these conditions are -4 and 3:
1. The product is -12: [tex]\(-4 \times 3 = -12\)[/tex]
2. The sum is -1: [tex]\(-4 + 3 = -1\)[/tex]
So, the quadratic [tex]\(x^2 - x - 12\)[/tex] can be factorized as [tex]\((x - 4)(x + 3)\)[/tex].
To model this factorization using algebra tiles:
- Negative unit tiles represent negative constants.
- Positive unit tiles represent positive constants.
From our factorization [tex]\((x - 4)(x + 3)\)[/tex], we notice:
- The term [tex]\(-4\)[/tex] indicates we need 4 negative unit tiles.
- The term [tex]\(3\)[/tex] indicates we need 3 positive unit tiles.
Thus, to complete the factorization modeled with algebra tiles, we need:
- 4 negative unit tiles and
- 3 positive unit tiles.
