Write the degree of each polynomial given below:

(i) xy + 7z

(ii) x² - 6x³ + 8

(iii) y - 6y² + 5y⁸

(iv) xyz - 3

(v) xy + yz² - zx³

(vi) x⁵y⁷ - 8x³y⁸ + 10x⁴y⁴z⁴

(i) Degree = 2
Reason — As the polynomial contains 3 variables, we will find the sum of powers of each term.
The sum of powers of the term xy = 1 + 1 = 2
The sum of powers of the term 7z = 1
∵ Highest sum of powers = 2
∴ Degree of polynomial = 2

(ii) Degree = 3
Reason — As the polynomial contains 1 variable, degree of a polynomial is the highest power of the variable in a polynomial expression.
Highest power of polynomial = 3
∴ Degree of polynomial = 3

(iii) Degree = 8
Reason — As the polynomial contains 1 variable, degree of a polynomial is the highest power of the variable in a polynomial expression.
Highest power of polynomial = 8
∴ Degree of polynomial = 8

(iv) Degree = 3
Reason — As the polynomial contains 3 variables, we will find the sum of powers of each term.
The sum of powers of the term xyz = 1 + 1 + 1 = 3
The powers of the term 3 = 0
∵ Highest sum of powers = 3
∴ Degree of polynomial = 3

(v) Degree = 4
Reason — As the polynomial contains 3 variables, we will find the sum of powers of each term.
The sum of powers of the term xy = 1 + 1 = 2
The sum of powers of the term yz² = 1 + 2 = 3
The sum of powers of the term zx³ = 1 + 3 = 4
∵ Highest sum of powers = 4
∴ Degree of polynomial = 4

(vi) Degree = 12
Reason — As the polynomial contains 3 variables, we will find the sum of powers of each term.
The sum of powers of the term x⁵y⁷ = 5 + 7 = 12
The sum of powers of the term - 8x³y⁸ = 3 + 8 = 11
The sum of powers of the term 10x⁴y⁴z⁴ = 4 + 4 + 4 = 12
∵ Highest sum of powers = 12
∴ Degree of polynomial = 12