Which expression is equivalent to x ^ 2 + 10x + 24 ?

Q
C (x + 3)(x + 8)
B (x + 2)(x + 12)
D (x + 4)(x + 6)
A (x + 1)(x + 24)

1 answer

To find the expression equivalent to \( x^2 + 10x + 24 \), we will factor the quadratic.

We need two numbers that multiply to \( 24 \) (the constant term) and add up to \( 10 \) (the coefficient of \( x \)).

The pairs of factors of \( 24 \) are:

  • \( 1 \times 24 = 24 \) (sums to 25)
  • \( 2 \times 12 = 24 \) (sums to 14)
  • \( 3 \times 8 = 24 \) (sums to 11)
  • \( 4 \times 6 = 24 \) (sums to 10)

The pair \( 4 \) and \( 6 \) add up to \( 10 \). Therefore, we can factor the expression as:

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

Thus, the correct answer is:

D. (x + 4)(x + 6)