Question

Use the polynomial identity  x2+2ax+a2=(x+a)(x+a)  to rewrite  x2+4x+4 . Which polynomial does this establish?(1 point)Responsesx2+4x+4=(x+2)(x+2)x squared plus 4 x plus 4 equals left parenthesis x plus 2 right parenthesis left parenthesis x plus 2 right parenthesisx2+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 parenthesisx2+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 parenthesisx2+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

Answer 1

To rewrite the polynomial \(x^2 + 4x + 4\) using the form \(x^2 + 2ax + a^2 = (x + a)(x + a)\), we need to identify \(a\).

In the expression \(x^2 + 4x + 4\):

- The coefficient of \(x\) is \(4\), which means \(2a = 4\). So, solving for \(a\), we have \(a = 2\).
- The constant term \(a^2\) should be \(4\) (since \(a = 2\), \(2^2 = 4\)).

Now, we can rewrite the polynomial as:

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

Thus, the established polynomial is:

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

So, the correct response is:

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