To determine a factor of the quadratic expression x² + 9x + 14, we can start by factoring it.
We need to find two numbers that multiply to +14 (the constant term) and add up to +9 (the coefficient of x). After evaluating the factors of 14, we find that the pair (2, 7) works because:
- 2 × 7 = 14
- 2 + 7 = 9
Using these numbers, we can rewrite the quadratic expression as:
x² + 2x + 7x + 14
Next, we group the terms:
(x² + 2x) + (7x + 14)
Factoring out the common factors gives:
x(x + 2) + 7(x + 2)
Now, we can factor out the common binomial factor (x + 2):
(x + 2)(x + 7)
Thus, one of the factors of the quadratic expression x² + 9x + 14 is (x + 2) or (x + 7).