To find the factors of the quadratic expression m² + 14m + 48, we need to factor it into the form (m + p)(m + q), where p and q are such that:
- p + q = 14 (the coefficient of m)
- p * q = 48 (the constant term)
Next, we need to identify two numbers that add up to 14 and multiply to 48. After considering the factor pairs of 48, we find:
- (6, 8)
Since 6 + 8 = 14 and 6 * 8 = 48, we can conclude that:
The expression factors to:
(m + 6)(m + 8)
To confirm, we can expand these factors:
(m + 6)(m + 8) = m² + 8m + 6m + 48 = m² + 14m + 48
This matches the original expression, which verifies our factorization. Therefore, the factors of the expression m² + 14m + 48 are: