Questions: Factor. s^2 + 4s + 4 Select the correct choice below and fill in any answer boxes with your answer. A. s^2 + 4s + 4 = □ B. The polynomial is prime.

Transcript text: Factor. \[ s^{2}+4 s+4 \] Select the correct choice below and fill in any answer boxes wi A. $s^{2}+4 s+4=$ $\square$ B. The polynomial is prime.

Solution

Solution Steps

To factor the given quadratic polynomial $ s^2 + 4s + 4 $, we need to find two binomials that multiply to give the original polynomial. We look for two numbers that multiply to the constant term (4) and add up to the coefficient of the linear term (4).

Step 1: Identify the Polynomial

We start with the polynomial $ s^2 + 4s + 4 $.

Step 2: Factor the Polynomial

To factor the polynomial, we look for two numbers that multiply to $ 4 $ (the constant term) and add up to $ 4 $ (the coefficient of the linear term). The numbers $ 2 $ and $ 2 $ satisfy these conditions.

Step 3: Write the Factored Form

Thus, we can express the polynomial as: \[ s^2 + 4s + 4 = (s + 2)(s + 2) = (s + 2)^2 \]