Find the degree of the polynomial
`9x^3-2x+17x^2y-y^4+14`

Answer

To find the degree of the polynomial \( 9x^3 - 2x + 17x^2y - y^4 + 14 \), we will follow these steps:

### Step 1: Identify the terms in the polynomial
The polynomial consists of the following terms:
- \( 9x^3 \)
- \( -2x \)
- \( 17x^2y \)
- \( -y^4 \)
- \( 14 \)

### Step 2: Determine the degree of each term
The degree of a term is the sum of the exponents of the variables in that term:
- For \( 9x^3 \): The degree is \( 3 \) (since \( x^3 \) has an exponent of 3).
- For \( -2x \): The degree is \( 1 \) (since \( x \) has an exponent of 1).
- For \( 17x^2y \): The degree is \( 2 + 1 = 3 \) (since \( x^2 \) has an exponent of 2 and \( y \) has an exponent of 1).
- For \( -y^4 \): The degree is \( 4 \) (since \( y^4 \) has an exponent of 4).
- For \( 14 \): The degree is \( 0 \) (since it is a constant term).

### Step 3: Identify the highest degree
Now, we compare the degrees of all the terms:
- \( 9x^3 \) has degree \( 3 \)
- \( -2x \) has degree \( 1 \)
- \( 17x^2y \) has degree \( 3 \)
- \( -y^4 \) has degree \( 4 \)
- \( 14 \) has degree \( 0 \)

The highest degree among these terms is \( 4 \) (from the term \( -y^4 \)).

### Conclusion
Thus, the degree of the polynomial \( 9x^3 - 2x + 17x^2y - y^4 + 14 \) is \( 4 \).

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