Write the degree of the given polynomials. i. √5 ii. x° iii. x2i

1.	Write the degree of the given polynomials. i. √5 ii. x° iii. x2iv. √2m10 – 7v. 2p – √7 vi. 7y – y3 + y5 vii. xyz + xy - z viii. m3n7– 3m5 n + mn
Answer» i. √5 = √5 x° ∴ Degree of the polynomial = 0 ii. x° ∴ Degree of the polynomial = 0 iii. x² ∴ Degree of the polynomial = 2 iv. √2m¹⁰ – 7 Here, the highest power of m is 10. ∴ Degree of the polynomial = 10 v. 2p – √7 Here, the highest power of p is 1. ∴ Degree of the polynomial = 1 vi. 7y – y³ + y⁵ Here, the highest power of y is 5. ∴ Degree of the polynomial = 5 vii. xyz + xy – z Here, the sum of the powers of x, y and z in the term xyz is 1 + 1 + 1 = 3, which is the highest sum of powers in the given polynomial. ∴ Degree of the polynomial = 3 viii. m³n⁷ – 3m⁵n + mn Here, the sum of the powers of m and n in the term m³ n⁷ is 3 + 7 = 10, which is the highest sum of powers in the given polynomial. ∴ Degree of the polynomial = 10

Write the degree of the given polynomials. i. √5 ii. x° iii. x2iv. √2m10 – 7v. 2p – √7 vi. 7y – y3 + y5 vii. xyz + xy - z viii. m3n7– 3m5 n + mn

Answer»

i. √5 = √5 x°

∴ Degree of the polynomial = 0

ii. x°

∴ Degree of the polynomial = 0

iii. x²

∴ Degree of the polynomial = 2

iv. √2m¹⁰ – 7

Here, the highest power of m is 10.

∴ Degree of the polynomial = 10

v. 2p – √7

Here, the highest power of p is 1.

∴ Degree of the polynomial = 1

vi. 7y – y³ + y⁵

Here, the highest power of y is 5.

∴ Degree of the polynomial = 5

vii. xyz + xy – z

Here, the sum of the powers of x, y and z in the term xyz is 1 + 1 + 1 = 3, which is the highest sum of powers in the given polynomial.

∴ Degree of the polynomial = 3

viii. m³n⁷ – 3m⁵n + mn

Here, the sum of the powers of m and n in the term m³ n⁷ is 3 + 7 = 10, which is the highest sum of powers in the given polynomial.

∴ Degree of the polynomial = 10