Degree of the polynomial `4x^(4)+0x^(3) +0x^(5) +5x+7 ` is

Options

A. 4
B. 5
C. 3
D. 7

Explanation

To find the degree of the polynomial \(4x^4 + 0x^3 + 0x^5 + 5x + 7\), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Polynomial**: The given polynomial is \(4x^4 + 0x^3 + 0x^5 + 5x + 7\).

2. **List the Terms**: The terms of the polynomial are:
- \(4x^4\)
- \(0x^3\)
- \(0x^5\)
- \(5x\)
- \(7\)

3. **Determine the Powers of Each Term**:
- The power of \(4x^4\) is \(4\).
- The power of \(0x^3\) is \(3\) (but since it is multiplied by \(0\), it does not contribute to the degree).
- The power of \(0x^5\) is \(5\) (but since it is multiplied by \(0\), it does not contribute to the degree).
- The power of \(5x\) is \(1\).
- The constant term \(7\) has a power of \(0\).

4. **Ignore Zero Coefficients**: Since \(0x^3\) and \(0x^5\) do not contribute to the polynomial, we can ignore them.

5. **Identify the Highest Power**: Now we look at the remaining terms:
- \(4x^4\) (power \(4\))
- \(5x\) (power \(1\))
- \(7\) (power \(0\))

The highest power among these is \(4\).

6. **Conclusion**: Therefore, the degree of the polynomial \(4x^4 + 0x^3 + 0x^5 + 5x + 7\) is \(4\).

### Final Answer:
The degree of the polynomial is \(4\).