Assertion : The degree of the polynomial `(x-2)(x-3)(x+4)` is `4` .
Reason : The number of zeroes of a polynomial is the degree of that polynomial .

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion .
B. If both assertion and reason are true but reason is not the correct explanation of assertion .
C. If assertion is true but reason is false .
D. If assertion is false but reason is true .

Answer

To solve the problem, we need to analyze the assertion and the reason provided.

### Step 1: Identify the polynomial
The polynomial given is \((x-2)(x-3)(x+4)\).

### Step 2: Determine the degree of the polynomial
The degree of a polynomial is determined by the highest power of \(x\) when the polynomial is fully expanded.

1. The polynomial is a product of three linear factors: \(x-2\), \(x-3\), and \(x+4\).
2. Each linear factor contributes a degree of 1.
3. Therefore, the total degree of the polynomial is the sum of the degrees of the individual factors:
\[ \text{Degree} = 1 + 1 + 1 = 3 \]

### Step 3: Verify the assertion
The assertion states that the degree of the polynomial is 4. From our calculation, we found that the degree is actually 3. Therefore, the assertion is **false**.

### Step 4: Analyze the reason
The reason states that "The number of zeroes of a polynomial is the degree of that polynomial."

1. A polynomial of degree \(n\) can have at most \(n\) real roots (or zeroes).
2. Since our polynomial is of degree 3, it can have up to 3 zeroes.
3. Therefore, the reason is **true**.

### Conclusion
- The assertion is **false**.
- The reason is **true**.

### Final Result
- Assertion: False
- Reason: True

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