Find the degree of the following polynomials.(i) x5 – x4 + 3(ii) 2

1.	Find the degree of the following polynomials.(i) x5 – x4 + 3(ii) 2 – y5 – y3 + 2y8(iii) 2(iv) 5x3 + 4x2 + 7x(v) 4xy + 7x2y + 3xy3
Answer» (i) x⁵ – x⁴ + 3 The terms of the given expression are x⁵, -x⁴, 3. Degree of each of the terms : 5, 4, 0 Term with highest degree: x⁵ Therefore degree of the expression in 5. (ii) 2 – y⁵ – y³ + 2y⁸ The terms of the given expression are 2, -y⁵ ,-y³, 2y⁸. Degree of each of the terms : 0, 2, 3, 8. Term with highest degree: 2y⁸ Therefore degree of the expression in 8. (iii) 2 Degree of the constant term is 0. ∴ Degree of 2 is 0. (iv) 5x³+ 4x² + 7x The terms of the given expression are 5x³, 4x², 7x Degree of each of the terms : 3, 2, 1 Term with highest degree: 5x³ Therefore degree of the expression in 3. (v) 4xy + 7x²y + 3xy³ The terms of the given expression are 4xy, 7x²y, 3xy³ Degree of each of the terms : 2, 3, 4 Term with highest degree: 3xy³ Therefore degree of the expression in 4.

Find the degree of the following polynomials.(i) x5 – x4 + 3(ii) 2 – y5 – y3 + 2y8(iii) 2(iv) 5x3 + 4x2 + 7x(v) 4xy + 7x2y + 3xy3

Answer»

(i) x⁵ – x⁴ + 3

The terms of the given expression are x⁵, -x⁴, 3.

Degree of each of the terms : 5, 4, 0

Term with highest degree: x⁵

Therefore degree of the expression in 5.

(ii) 2 – y⁵ – y³ + 2y⁸

The terms of the given expression are 2, -y⁵ ,-y³, 2y⁸.

Degree of each of the terms : 0, 2, 3, 8.

Term with highest degree: 2y⁸

Therefore degree of the expression in 8.

(iii) 2

Degree of the constant term is 0.

∴ Degree of 2 is 0.

(iv) 5x³+ 4x² + 7x

The terms of the given expression are 5x³, 4x², 7x

Degree of each of the terms : 3, 2, 1

Term with highest degree: 5x³

Therefore degree of the expression in 3.

(v) 4xy + 7x²y + 3xy³

The terms of the given expression are 4xy, 7x²y, 3xy³

Degree of each of the terms : 2, 3, 4

Term with highest degree: 3xy³

Therefore degree of the expression in 4.