Write the degree fo the following polynomials.
(i)`3x^(5)-7x^(2)+8x-2x^(2)+10`
`(ii) 2x^(9)-3x^(2)-14x^(3)-15x^(4)`

Explanation

To find the degree of the given polynomials, we need to identify the term with the highest power of the variable \( x \) in each polynomial. The degree of a polynomial is defined as the highest exponent of the variable in the polynomial.

Let's solve the problem step by step.

### Step 1: Identify the first polynomial
The first polynomial is:
\[ 3x^{5} - 7x^{2} + 8x - 2x^{2} + 10 \]

### Step 2: Simplify the first polynomial
Combine like terms:
- The terms with \( x^2 \) are \( -7x^2 \) and \( -2x^2 \).
- Combine them:
\[ -7x^2 - 2x^2 = -9x^2 \]
So, the polynomial simplifies to:
\[ 3x^{5} - 9x^{2} + 8x + 10 \]

### Step 3: Determine the highest degree in the first polynomial
Now, we look at the degrees of each term:
- The degree of \( 3x^{5} \) is 5.
- The degree of \( -9x^{2} \) is 2.
- The degree of \( 8x \) is 1.
- The degree of \( 10 \) (constant term) is 0.

The highest degree is 5. Therefore, the degree of the first polynomial is:
\[ \text{Degree of the first polynomial} = 5 \]

### Step 4: Identify the second polynomial
The second polynomial is:
\[ 2x^{9} - 3x^{2} - 14x^{3} - 15x^{4} \]

### Step 5: Determine the highest degree in the second polynomial
Now, we look at the degrees of each term:
- The degree of \( 2x^{9} \) is 9.
- The degree of \( -3x^{2} \) is 2.
- The degree of \( -14x^{3} \) is 3.
- The degree of \( -15x^{4} \) is 4.

The highest degree is 9. Therefore, the degree of the second polynomial is:
\[ \text{Degree of the second polynomial} = 9 \]

### Final Answer
- The degree of the first polynomial is **5**.
- The degree of the second polynomial is **9**.

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