Which of the following is the correct factorization of x^2 + 5x + 6?

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Question: Which of the following is the correct factorization of x^2 + 5x + 6?

Options:

Correct Answer: (x + 2)(x + 3)

Solution:

Step 1: Find two numbers that multiply to 6 and add to 5: 2 and 3. Step 2: Factor as (x + 2)(x + 3).

Which of the following is the correct factorization of x^2 + 5x + 6?

Which of the following is the correct factorization of x^2 + 5x + 6?

Step 1: Look at the constant term in the expression, which is 6. We need to find two numbers that multiply together to give 6.
Step 2: Think of pairs of numbers that multiply to 6. The pairs are (1, 6) and (2, 3).
Step 3: Now, we need to check which of these pairs adds up to the coefficient of the x term, which is 5.
Step 4: The pair (2, 3) adds up to 5 (2 + 3 = 5). So, we will use these numbers.
Step 5: Write the expression in factored form using the numbers we found: (x + 2)(x + 3).

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