Question
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)
Q
C (x + 3)(x + 8)
B (x + 2)(x + 12)
D (x + 4)(x + 6)
A (x + 1)(x + 24)
Answers
GPT-4o mini
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)**
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)**