If `x^3-3x^2+3x+7=(x+1)(a x^2+b x+c),\ ` then `a+b+c=` (a)4 (b) 12 (c) `-10\ ` (d) 3

Explanation

To solve the equation \( x^3 - 3x^2 + 3x + 7 = (x + 1)(ax^2 + bx + c) \) and find the value of \( a + b + c \), we will follow these steps:

### Step 1: Polynomial Division
We will divide \( x^3 - 3x^2 + 3x + 7 \) by \( x + 1 \).

1. **Divide the leading term**: \( \frac{x^3}{x} = x^2 \).
2. **Multiply**: \( x^2 \cdot (x + 1) = x^3 + x^2 \).
3. **Subtract**:
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