Question

Use the table to identify values of p and q that can be used to factor x2 – x – 12 as (x + p)(x + q).



p q p + q
2 -6 -4
-2 6 4
3 -4 -1
-3 4 1


The factors that can be used are _____

Answer 1

To factor the quadratic \( x^2 - x - 12 \) as \( (x + p)(x + q) \), we need to find values of \( p \) and \( q \) such that:

1. \( p + q = -1 \) (the coefficient of \( x \))
2. \( p \cdot q = -12 \) (the constant term)

Let's look at the values in the table:

- For \( p = 2 \) and \( q = -6 \):
- \( p + q = 2 - 6 = -4 \) (not correct)
- \( p \cdot q = 2 \cdot (-6) = -12 \) (correct)

- For \( p = -2 \) and \( q = 6 \):
- \( p + q = -2 + 6 = 4 \) (not correct)
- \( p \cdot q = -2 \cdot 6 = -12 \) (correct)

- For \( p = 3 \) and \( q = -4 \):
- \( p + q = 3 - 4 = -1 \) (correct)
- \( p \cdot q = 3 \cdot (-4) = -12 \) (correct)

- For \( p = -3 \) and \( q = 4 \):
- \( p + q = -3 + 4 = 1 \) (not correct)
- \( p \cdot q = -3 \cdot 4 = -12 \) (correct)

The only pair that satisfies both conditions is \( p = 3 \) and \( q = -4 \).

Thus, the factors that can be used are \( (x + 3)(x - 4) \).