If `P(x) =x+3,` then `p(x)+p(-x) ` is equal to

Options

A. 3
B. 2x
C. zero
D. 6

Explanation

To solve the problem, we need to find the value of \( P(x) + P(-x) \) given that \( P(x) = x + 3 \).

### Step-by-Step Solution:

1. **Identify \( P(x) \)**:
We are given that \( P(x) = x + 3 \).

2. **Find \( P(-x) \)**:
To find \( P(-x) \), we substitute \(-x\) into the polynomial \( P(x) \):
\[ P(-x) = -x + 3 \]

3. **Add \( P(x) \) and \( P(-x) \)**:
Now we need to compute \( P(x) + P(-x) \):
\[ P(x) + P(-x) = (x + 3) + (-x + 3) \]

4. **Simplify the Expression**:
Combine like terms:
\[ P(x) + P(-x) = x + 3 - x + 3 \]
The \( x \) and \(-x\) cancel each other out:
\[ = 3 + 3 = 6 \]

5. **Final Answer**:
Therefore, \( P(x) + P(-x) = 6 \).