Find the degree of the polynomial `4x^(5)-2x^(2)y^(3)+6`.

Options

A. 3
B. 4
C. 5
D. 6

Answer

To find the degree of the polynomial \( 4x^5 - 2x^2y^3 + 6 \), we will follow these steps:

### Step 1: Identify the terms of the polynomial
The polynomial consists of three terms:
1. \( 4x^5 \)
2. \( -2x^2y^3 \)
3. \( 6 \)

### Step 2: Determine the degree of each term
- The degree of the first term \( 4x^5 \) is 5, since the exponent of \( x \) is 5.
- The degree of the second term \( -2x^2y^3 \) is calculated by adding the exponents of \( x \) and \( y \): \( 2 + 3 = 5 \).
- The degree of the third term \( 6 \) is 0, as it is a constant term.

### Step 3: Find the highest degree among the terms
Now, we compare the degrees of all the terms:
- Degree of \( 4x^5 \) is 5.
- Degree of \( -2x^2y^3 \) is also 5.
- Degree of \( 6 \) is 0.

The highest degree among these is 5.

### Step 4: Conclude the degree of the polynomial
Therefore, the degree of the polynomial \( 4x^5 - 2x^2y^3 + 6 \) is 5.

### Final Answer
The degree of the polynomial is **5**.

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