Kristina factored the trinomial on her whiteboard.

Question

x2 + 10x + 24

Which expression is equivalent?

Group of answer choices

(x + 2)(x + 12)

(x + 1)(x + 24)

(x + 4)(x + 6)

(x + 3)(x + 8)

Answer 1

To factor the trinomial \( x^2 + 10x + 24 \), we need to find two numbers that multiply to 24 (the constant term) and add up to 10 (the coefficient of the linear term).

The pairs of factors of 24 are:

• (1, 24)
• (2, 12)
• (3, 8)
• (4, 6)

Among these pairs, we see that \( 4 \) and \( 6 \) add up to \( 10 \).

Thus, we can factor the trinomial as: \[ (x + 4)(x + 6) \]

Therefore, the equivalent expression for the trinomial \( x^2 + 10x + 24 \) is: \[ \boxed{(x + 4)(x + 6)} \]