Find the degree of the polynomial `8x^(4) + 2x^(2) y^(3) + 4 `

Options

A. 4
B. 5
C. 0
D. 1

Answer

To find the degree of the polynomial \(8x^4 + 2x^2y^3 + 4\), we will follow these steps:

### Step 1: Identify the terms of the polynomial
The polynomial consists of three terms:
1. \(8x^4\)
2. \(2x^2y^3\)
3. \(4\)

### Step 2: Determine the degree of each term
- The degree of a term in a polynomial is the sum of the exponents of the variables in that term.

1. **For the first term \(8x^4\)**:
- The exponent of \(x\) is \(4\).
- There are no other variables, so the degree is \(4\).

2. **For the second term \(2x^2y^3\)**:
- The exponent of \(x\) is \(2\) and the exponent of \(y\) is \(3\).
- The degree is \(2 + 3 = 5\).

3. **For the third term \(4\)**:
- This is a constant term, and the degree of a constant is \(0\).

### Step 3: Find the highest degree among the terms
Now we compare the degrees of all the terms:
- Degree of \(8x^4\) is \(4\).
- Degree of \(2x^2y^3\) is \(5\).
- Degree of \(4\) is \(0\).

The highest degree among these is \(5\).

### Conclusion
The degree of the polynomial \(8x^4 + 2x^2y^3 + 4\) is \(5\).

---