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

For example :

(a) 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

(b) The degree of polynomial :

(i) 4y^{3} – 3y + 8 is 3

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

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

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

(i) 3x^{2}– 5x

(ii) x +

(iii) √m – 8

(iv) z^{5}– z^{1/3}+ 8

**Solution:**

(i) 3x^{2} – 5x = 3x^{2} – 5x^{1}. It is a polynomial.

(ii) x + = x1 + x^{–1}. It is not a polynomial.

(iii) √m – 8 = y^{1/2} – 8. Since, the power of the first term (√m) is 1/2, which is not a whole number. Hence, it is not a polynomial.

(iv) z^{5} – z^{1/3 }+ 8 = z5 – 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: 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

Solution:

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

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