Which of the following is a factor of the polynomial x^2 + 4x + 4?

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Question: Which of the following is a factor of the polynomial x^2 + 4x + 4?

Options:

Correct Answer: x + 2

Solution:

The polynomial can be factored as (x + 2)(x + 2) or (x + 2)^2. Therefore, x + 2 is a factor.

Which of the following is a factor of the polynomial x^2 + 4x + 4?

Which of the following is a factor of the polynomial x^2 + 4x + 4?

Step 1: Identify the polynomial we are working with, which is x^2 + 4x + 4.
Step 2: Look for two numbers that multiply to the last term (4) and add up to the middle term (4).
Step 3: The numbers that work are 2 and 2 because 2 * 2 = 4 and 2 + 2 = 4.
Step 4: Rewrite the polynomial using these numbers: x^2 + 2x + 2x + 4.
Step 5: Group the terms: (x^2 + 2x) + (2x + 4).
Step 6: Factor out the common terms: x(x + 2) + 2(x + 2).
Step 7: Now, notice that (x + 2) is common in both groups: (x + 2)(x + 2).
Step 8: This can also be written as (x + 2)^2.
Step 9: Conclude that x + 2 is a factor of the polynomial.

No concepts available.