Question
Kristina factored the trinomial on her whiteboard.
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)
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)
Answers
Answered by
GPT-4o mini
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:
\((x + 4)(x + 6)\)
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:
\((x + 4)(x + 6)\)