Which of the following polynomials is a perfect square?

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Question: Which of the following polynomials is a perfect square?

Options:

Correct Answer: x^2 + 4x + 4

Solution:

The polynomial x^2 + 4x + 4 can be factored as (x + 2)^2, making it a perfect square.

Which of the following polynomials is a perfect square?

Which of the following polynomials is a perfect square?

Step 1: Identify the polynomial you want to check. In this case, it is x^2 + 4x + 4.
Step 2: Look for a way to factor the polynomial. A perfect square polynomial can be written in the form (a + b)^2.
Step 3: Check if the polynomial can be expressed as (x + b)^2. Here, we need to find b.
Step 4: Notice that the first term is x^2, which suggests that the first part of the factor is x.
Step 5: The last term is 4, which is 2^2. This suggests that b could be 2.
Step 6: Write the polynomial as (x + 2)(x + 2) to see if it matches the original polynomial.
Step 7: Expand (x + 2)(x + 2) to check: x^2 + 2x + 2x + 4 = x^2 + 4x + 4.
Step 8: Since the expanded form matches the original polynomial, we conclude that x^2 + 4x + 4 is a perfect square.

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