Factor x^2 + 11x + 24.
A. (x + 6) (x + 4)
B. (x + 2) (x + 12)
C. (x + 3) (x + 8)
D. (x + 1) (x + 11)
To factor the quadratic expression x^2 + 11x + 24, we need to find two binomials that when multiplied together will give us the original expression.
The binomials will have the form (x + m) (x + n), where m and n are two numbers that when multiplied together will give us 24, and when added together will give us 11.
Let's find two numbers that satisfy these conditions:
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, and 24.
Let's test some pairs of numbers:
For (m, n) = (1, 24), we have 1 + 24 = 25, which is not 11.
For (m, n) = (2, 12), we have 2 + 12 = 14, which is not 11.
For (m, n) = (3, 8), we have 3 + 8 = 11, which is the number we want!
Therefore, the correct factors of x^2 + 11x + 24 are (x + 3) (x + 8).