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 will follow these steps:

### Step 1: Identify the Terms
The polynomial consists of several terms:
- \(4x^{4}\)
- \(0x^{3}\)
- \(0x^{5}\)
- \(5x\)
- \(7\)

### Step 2: Determine the Degree of Each Term
The degree of a term is determined by the exponent of the variable \(x\) in that term:
- The term \(4x^{4}\) has a degree of \(4\).
- The term \(0x^{3}\) has a degree of \(3\), but since the coefficient is \(0\), this term does not contribute to the degree of the polynomial.
- The term \(0x^{5}\) has a degree of \(5\), but again, since the coefficient is \(0\), this term does not contribute to the degree of the polynomial.
- The term \(5x\) has a degree of \(1\).
- The constant term \(7\) has a degree of \(0\).

### Step 3: Identify the Highest Degree
Now, we need to find the highest degree among the non-zero terms:
- The degrees of the non-zero terms are \(4\) (from \(4x^{4}\)), \(1\) (from \(5x\)), and \(0\) (from \(7\)).
- The highest degree is \(4\).

### Step 4: Conclusion
Thus, the degree of the polynomial \(4x^{4} + 0x^{3} + 0x^{5} + 5x + 7\) is \(4\).

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

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