Use the polynomial identity x2+2ax+a2=(x+a)(x+a) to rewrite x2+4x+4 . Which polynomial does this establish?(1 point)

Question

Responses

x2+4x+4=(x+4)(x+4)
x squared plus 4 x plus 4 equals left parenthesis x plus 4 right parenthesis left parenthesis x plus 4 right parenthesis

x2+4x+4=(x−4)(x−4)
x squared plus 4 x plus 4 equals left parenthesis x minus 4 right parenthesis left parenthesis x minus 4 right parenthesis

x2+4x+4=(x−2)(x−2)
x squared plus 4 x plus 4 equals left parenthesis x minus 2 right parenthesis left parenthesis x minus 2 right parenthesis

x2+4x+4=(x+2)(x+2)

Answer 1

To rewrite the polynomial \( x^2 + 4x + 4 \) using the given identity \( x^2 + 2ax + a^2 = (x + a)(x + a) \), we need to identify \( a \) in our expression.

We can rewrite \( x^2 + 4x + 4 \) in the form of the identity:

1. The term \( 2a \) corresponds to \( 4 \) (the coefficient of \( x \)). Thus, we can set \( 2a = 4 \), which gives us \( a = 2 \).
2. The term \( a^2 \) corresponds to \( 4 \), and since \( a = 2 \), we have \( a^2 = 2^2 = 4 \).

Thus, we can rewrite the polynomial as follows:

\[ x^2 + 4x + 4 = (x + 2)(x + 2) \]

So the correct response is:

\( x^2 + 4x + 4 = (x + 2)(x + 2) \)

In text format, this is:

\( x^2 + 4x + 4 = (x + 2)(x + 2) \)