Write the degree of each polynomials given below :
`y - 6y^(2) + 5y^(8)`

Options

A. 8
B. 2
C. 7
D. 11

Answer

To find the degree of the polynomial \( y - 6y^{2} + 5y^{8} \), we will follow these steps:

### Step 1: Identify the terms in the polynomial
The given polynomial is:
\[ y - 6y^{2} + 5y^{8} \]
This polynomial consists of three terms:
1. \( y \)
2. \( -6y^{2} \)
3. \( 5y^{8} \)

### Step 2: Determine the power of the variable in each term
Now, we will find the power of the variable \( y \) in each term:
- In the term \( y \), the power of \( y \) is \( 1 \) (since \( y = y^{1} \)).
- In the term \( -6y^{2} \), the power of \( y \) is \( 2 \).
- In the term \( 5y^{8} \), the power of \( y \) is \( 8 \).

### Step 3: Identify the maximum power
Next, we will identify the maximum power among the powers we found:
- The powers are \( 1, 2, \) and \( 8 \).
- The maximum power is \( 8 \).

### Step 4: Conclude the degree of the polynomial
The degree of the polynomial is the maximum power of the variable, which we found to be \( 8 \).

Thus, the degree of the polynomial \( y - 6y^{2} + 5y^{8} \) is:
\[ \text{Degree} = 8 \]

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