The greatest power (exponent) of the terms of a polynomial is called degree of the polynomial.
For example :
(a) In polynomial 5x2 – 8x7 + 3x :
(i) The power of term 5x2 = 2
(ii) The power of term –8x7 = 7
(iii) The power of 3x = 1
Since, the greatest power is 7, therefore degree of the polynomial 5x2 – 8x7 + 3x is 7
(b) The degree of polynomial :
(i) 4y3 – 3y + 8 is 3
(ii) 7p + 2 is 1 since (p = p1)
(iii) 2m – 7m8 + m13 is 13 and so on.
Example : Find which of the following algebraic expression is a polynomial.
(i) 3x2 – 5x
(ii) x +
(iii) √m – 8
(iv) z5 – z1/3 + 8
(i) 3x2 – 5x = 3x2 – 5x1. It is a polynomial.
(ii) x + = x1 + x–1. It is not a polynomial.
(iii) √m – 8 = y1/2 – 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) z5 – z1/3 + 8 = z5 – z1/3 + 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 – 6x3 + 8x7 + 6x2
(ii) 2y12 + 3y10 – y15 + y + 3
(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 = x1 ↠ degree is 1.
(iv) 8 = 8x0 ↠ degree = 0