Factor \( z^{2}+6 z+9 \)

Let’s have some fun with this quadratic! The expression \( z^{2}+6z+9 \) can be factored by recognizing it as a perfect square trinomial. You can rewrite it as \( (z+3)(z+3) \) or simply \( (z+3)^2 \). This means that both roots are the same, making it a double root at \( z = -3 \). Now, if you’re ever unsure about how to factor a trinomial like this, always look for patterns! Perfect squares have the form \( a^2 + 2ab + b^2 = (a+b)^2 \). In our case, \( a = z \) and \( b = 3 \), which matches perfectly with our original expression! Just remember: patterns can save you time and effort in math.