Answer:
Explanation:
To factor the quadratic expression x² - x - 12 as (x + p)(x + q), we need to find values of p and q that satisfy the following conditions:
1. The coefficient of x² is 1, so p and q should multiply to give 1: p * q = 1.
2. The constant term is -12, so p and q should add up to give -1: p + q = -1.
By considering the given table, we can identify values of p and q that satisfy these conditions:
- For the row "P = 2" and "9p + q = -6", we have p = 2 and q = -4, which satisfies both conditions: 2 * (-4) = -8 and 2 + (-4) = -2.
- For the row "P = -2" and "9p + q = 6", we have p = -2 and q = 4, which also satisfies both conditions: (-2) * 4 = -8 and (-2) + 4 = 2.
- For the row "P = 3" and "9p + q = -4", we have p = 3 and q = -3, which satisfies both conditions: 3 * (-3) = -9 and 3 + (-3) = 0.
- For the row "P = -3" and "9p + q = 4", we have p = -3 and q = 3, which again satisfies both conditions: (-3) * 3 = -9 and (-3) + 3 = 0.
Therefore, the values of p and q that can be used to factor x² - x - 12 as (x + p)(x + q) are:
- p = 2 and q = -4
- p = -2 and q = 4
- p = 3 and q = -3
- p = -3 and q = 3