Question
Factor the perfect square.
4 x squared plus 4 x plus 1
Question content area bottom
Part 1
Select the correct choice below and, if necessary, fill in the answer box within your choice.
A.4 x squared plus 4 x plus 1 equals enter your response here
4 x squared plus 4 x plus 1equals
enter your response here
B.
The polynomial is prime
4 x squared plus 4 x plus 1
Question content area bottom
Part 1
Select the correct choice below and, if necessary, fill in the answer box within your choice.
A.4 x squared plus 4 x plus 1 equals enter your response here
4 x squared plus 4 x plus 1equals
enter your response here
B.
The polynomial is prime
Answers
Answered by
GPT-4o mini
To factor the expression \(4x^2 + 4x + 1\), we can observe that it has the form of a perfect square trinomial.
We can rewrite \(4x^2 + 4x + 1\) as:
\[
(2x + 1)^2
\]
Here's how we see this:
1. \( (2x)^2 = 4x^2 \)
2. \( 2 \cdot (2x) \cdot 1 = 4x \)
3. \( 1^2 = 1 \)
Thus, the equation can be factored as:
\[
4x^2 + 4x + 1 = (2x + 1)^2
\]
So the correct choice is:
A. \( 4x^2 + 4x + 1 = (2x + 1)^2 \)
We can rewrite \(4x^2 + 4x + 1\) as:
\[
(2x + 1)^2
\]
Here's how we see this:
1. \( (2x)^2 = 4x^2 \)
2. \( 2 \cdot (2x) \cdot 1 = 4x \)
3. \( 1^2 = 1 \)
Thus, the equation can be factored as:
\[
4x^2 + 4x + 1 = (2x + 1)^2
\]
So the correct choice is:
A. \( 4x^2 + 4x + 1 = (2x + 1)^2 \)