Final answer:
The value of b that makes the quadratic y² + by − 24 factorable is 5. This is because the factors of -24 that add up to 5 are 8 and -3. Therefore, the quadratic can be factored as (y + 8)(y - 3).
Step-by-step explanation:
The question seeks to determine which value of b would make the quadratic y² + by − 24 factorable. To factor a quadratic equation, we look for two numbers that multiply to the constant term (in this case, -24) and add up to the coefficient of the middle term (b).
Let's consider the options:
- For A. 14, the numbers could be 6 and -4, since 6 × -4 = -24 and 6 + (-4) = 2, not 14.
- For B. 11, the numbers could be 8 and -3, since 8 × -3 = -24 and 8 + (-3) = 5, not 11.
- For C. 5, the numbers could be 8 and -3, since 8 × -3 = -24 and 8 + (-3) = 5, which matches option C.
- For D. 25, the numbers could be 1 and -24, since 1 × -24 = -24 and 1 + (-24) = -23, not 25.
Therefore, the correct answer is C. 5, as it is the value of b that allows the quadratic to be factorable as (y + 8)(y - 3).