Which of the following is a zero of the polynomial `x^(2)+6x+9` ?

Options

A. 2
B. `-1`
C. `-3`
D. 0

Answer

To determine which of the following is a zero of the polynomial \( x^2 + 6x + 9 \), we can follow these steps:

### Step 1: Identify the polynomial
We start with the polynomial:
\[ x^2 + 6x + 9 \]

### Step 2: Recognize the form of the polynomial
Notice that this polynomial can be expressed in a different form. We can see that it resembles the perfect square trinomial:
\[ a^2 + 2ab + b^2 = (a + b)^2 \]
where \( a = x \) and \( b = 3 \).

### Step 3: Rewrite the polynomial
Using the identity for perfect squares, we can rewrite the polynomial:
\[ x^2 + 6x + 9 = (x + 3)^2 \]

### Step 4: Set the polynomial equal to zero
To find the zeros of the polynomial, we set it equal to zero:
\[ (x + 3)^2 = 0 \]

### Step 5: Solve for \( x \)
Taking the square root of both sides, we get:
\[ x + 3 = 0 \]
Subtracting 3 from both sides gives:
\[ x = -3 \]

### Conclusion
Thus, the zero of the polynomial \( x^2 + 6x + 9 \) is:
\[ \boxed{-3} \]

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