Questions: Factor the perfect square trinomial. x^2+4 x+4 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. x^2+4 x+4= (Factor completely.) B. The polynomial is prime.

Solution Steps

The given trinomial is \( x^{2} + 4x + 4 \). A perfect square trinomial has the form \( (x + a)^{2} = x^{2} + 2ax + a^{2} \).

Compare \( x^{2} + 4x + 4 \) with \( x^{2} + 2ax + a^{2} \). Here, \( 2a = 4 \) and \( a^{2} = 4 \).

From \( 2a = 4 \), we get \( a = 2 \). Substituting \( a = 2 \) into \( a^{2} \), we get \( a^{2} = 4 \), which matches the constant term in the trinomial.

Since the trinomial matches the perfect square form, it can be factored as \( (x + 2)^{2} \).

The correct choice is A, and the factored form is \( (x + 2)^{2} \).

Final Answer