Find the degree of each of the following polynomials :
`(i) 3x^(4)-x^(2)+8 " " (ii) y^(2)-5y+7 " " (iii) 3x+4 " " (iv) 3`
`(v) x-2x^(2)+5x^(7) " " (vi) 2y^(2)-5y^(6)+1 " "(vii) x^(3)-1 " " (viii) 3x+5x^(5)+1`

Answer

To find the degree of each polynomial, we need to identify the highest power of the variable in each expression. Let's solve each part step by step.

### Solution:

**(i)** For the polynomial \(3x^4 - x^2 + 8\):
- The terms are \(3x^4\), \(-x^2\), and \(8\).
- The highest power of \(x\) is \(4\).
- **Degree**: \(4\)

**(ii)** For the polynomial \(y^2 - 5y + 7\):
- The terms are \(y^2\), \(-5y\), and \(7\).
- The highest power of \(y\) is \(2\).
- **Degree**: \(2\)

**(iii)** For the polynomial \(3x + 4\):
- The terms are \(3x\) and \(4\).
- The highest power of \(x\) is \(1\).
- **Degree**: \(1\)

**(iv)** For the polynomial \(3\):
- This is a constant term, which can be considered as \(3x^0\).
- The highest power of \(x\) is \(0\).
- **Degree**: \(0\)

**(v)** For the polynomial \(x - 2x^2 + 5x^7\):
- The terms are \(x\), \(-2x^2\), and \(5x^7\).
- The highest power of \(x\) is \(7\).
- **Degree**: \(7\)

**(vi)** For the polynomial \(2y^2 - 5y^6 + 1\):
- The terms are \(2y^2\), \(-5y^6\), and \(1\).
- The highest power of \(y\) is \(6\).
- **Degree**: \(6\)

**(vii)** For the polynomial \(x^3 - 1\):
- The terms are \(x^3\) and \(-1\).
- The highest power of \(x\) is \(3\).
- **Degree**: \(3\)

**(viii)** For the polynomial \(3x + 5x^5 + 1\):
- The terms are \(3x\), \(5x^5\), and \(1\).
- The highest power of \(x\) is \(5\).
- **Degree**: \(5\)

### Summary of Degrees:
1. \(4\)
2. \(2\)
3. \(1\)
4. \(0\)
5. \(7\)
6. \(6\)
7. \(3\)
8. \(5\)