## Degree Of A Polynomial

The greatest power (exponent) of the terms of a polynomial is called degree of the polynomial.

For example :

In polynomial 5x^{2} – 8x^{7} + 3x:

(i) The power of term 5x^{2} = 2

(ii) The power of term –8x^{7} = 7

(iii) The power of 3x = 1

Since, the greatest power is 7, therefore degree of the polynomial 5x^{2} – 8x^{7} + 3x is 7

The degree of polynomial :

(i) 4y^{3} – 3y + 8 is 3

(ii) 7p + 2 is 1(p = p^{1})

(iii) 2m – 7m^{8} + m^{13} is 13 and so on.

## Degree Of A Polynomial With Example Problems With Solutions

**Example 1: **Find which of the following algebraic expression is a polynomial.

(i) 3x^{2} – 5x (ii) \(\text{x + }\frac{1}{\text{x}}\) (iii) √y– 8 (iv) z^{5} – ∛z + 8

**Sol.**

(i) 3x^{2} – 5x = 3x^{2} – 5x^{1}

It is a polynomial.

(ii) \(\text{x + }\frac{1}{\text{x}}\) = x^{1} + x^{-1}

It is not a polynomial.

(iii) √y– 8 = y^{1/2}– 8

Since, the power of the first term (√y) is \(\frac{1}{2}\), which is not a whole number.

(iv) z^{5} – ∛z + 8 = z^{5} – z^{1/3} + 8

Since, the exponent of the second term is 1/3, which in not a whole number. Therefore, the given expression is not a polynomial.

**Example 2: **Find the degree of the polynomial :

(i) 5x – 6x^{3} + 8x^{7} + 6x^{2} (ii) 2y^{12} + 3y^{10} – y^{15} + y + 3 (iii) x (iv) 8

**Sol.**

(i)** **Since the term with highest exponent (power) is 8x^{7} and its power is 7.

∴ The degree of given polynomial is 7.

(ii) The highest power of the variable is 15

∴ degree = 15

(iii) x = x^{1} ⇒ degree is 1.

(iv) 8 = 8x^{0} ⇒ degree = 0