Kristina factored the trinomial on her whiteboard.

Question

x2 + 10x + 24

Which expression is equivalent?

Group of answer choices

(x + 3)(x + 8)

(x + 2)(x + 12)

(x + 4)(x + 6)

(x + 1)(x + 24)

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 numbers that satisfy these conditions are 4 and 6 because:

• \(4 \times 6 = 24\)
• \(4 + 6 = 10\)

Therefore, we can factor the trinomial as follows:

\[ x^2 + 10x + 24 = (x + 4)(x + 6) \]

Among the given choices, the equivalent expression is:

\((x + 4)(x + 6)\)

So, the answer is: \((x + 4)(x + 6)\)