Gaurav traveled `(p^(2)-4p+2)` kilomeres by car and `(2p^(2)+6p-5)` kilometres by bus. What is the total distance travelled by Gaurav?

Options

A. `(p^(2)+2p-3)`km
B. `(3p^(2)-3p-3)`km
C. `(3p^(2)+2p-3)`km
D. `3(p^(2)-p-1)`km

Answer

To find the total distance traveled by Gaurav, we need to add the distances he traveled by car and by bus. The distances are given as:

- Distance traveled by car: \( p^2 - 4p + 2 \) kilometers
- Distance traveled by bus: \( 2p^2 + 6p - 5 \) kilometers

### Step-by-Step Solution:

1. **Write down the distances:**
- Distance by car: \( p^2 - 4p + 2 \)
- Distance by bus: \( 2p^2 + 6p - 5 \)

2. **Add the two distances together:**
\[ \text{Total Distance} = (p^2 - 4p + 2) + (2p^2 + 6p - 5) \]

3. **Combine like terms:**
- Combine the \( p^2 \) terms:
\[ p^2 + 2p^2 = 3p^2 \]
- Combine the \( p \) terms:
\[ -4p + 6p = 2p \]
- Combine the constant terms:
\[ 2 - 5 = -3 \]

4. **Write the combined expression:**
\[ \text{Total Distance} = 3p^2 + 2p - 3 \]

5. **Final Answer:**
The total distance traveled by Gaurav is:
\[ \boxed{3p^2 + 2p - 3} \text{ kilometers} \]