For a polynomial `p(x)` of degree `ge1, p(a)=0` , where a is a real number, then `(x-a)` is a factor of the polynomial `p(x)`
`p(x)=x^(3)-3x^(2)+4x-12` , then `p(3)` is

Options

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

Answer

To find \( p(3) \) for the polynomial \( p(x) = x^3 - 3x^2 + 4x - 12 \), we will substitute \( x = 3 \) into the polynomial and simplify.

### Step-by-step Solution:

1. **Write down the polynomial**:
\[ p(x) = x^3 - 3x^2 + 4x - 12 \]

2. **Substitute \( x = 3 \)**:
\[ p(3) = 3^3 - 3(3^2) + 4(3) - 12 \]

3. **Calculate \( 3^3 \)**:
\[ 3^3 = 27 \]

4. **Calculate \( 3(3^2) \)**:
\[ 3^2 = 9 \quad \Rightarrow \quad 3(3^2) = 3 \times 9 = 27 \]

5. **Calculate \( 4(3) \)**:
\[ 4(3) = 12 \]

6. **Substitute these values back into the polynomial**:
\[ p(3) = 27 - 27 + 12 - 12 \]

7. **Simplify the expression**:
\[ p(3) = 27 - 27 + 12 - 12 = 0 + 0 = 0 \]

Thus, \( p(3) = 0 \).

### Final Answer:
\[ p(3) = 0 \]