To factor the quadratic expression x² + 14x + 48, we want to find two numbers that multiply to the constant term (48) and add up to the coefficient of the linear term (14).
Let’s analyze the factors of 48:
- 1 and 48
- 2 and 24
- 3 and 16
- 4 and 12
- 6 and 8
Now, we need to determine which pair of factors also adds up to 14. If we examine the pairs:
- 1 + 48 = 49
- 2 + 24 = 26
- 3 + 16 = 19
- 4 + 12 = 16
- 6 + 8 = 14
We find that the pair 6 and 8 meets our criteria because:
- 6 × 8 = 48
- 6 + 8 = 14
Thus, we can rewrite the quadratic expression in its factored form:
x² + 14x + 48 = (x + 6)(x + 8)
In conclusion, the expression x² + 14x + 48 factors to (x + 6)(x + 8).