0look at the polynomial p(x) = 3x7 – 4x6 + x + 9. What is the term with the highest power of x ? It is 3x7.
The exponent of x in this term is 7. Similarly, in the polynomial q(y) = 5y6 – 4y2 – 6, the term with the highest power of y is 5y6 and the exponent of y in this term is 6. We call the highest power of the variable in a polynomial as the degree of the polynomial. So, the degree of the polynomial 3x7 – 4x6 + x + 9 is 7 and the degree of the polynomial 5y6 – 4y2 – 6 is 6. The degree of a non-zero constant polynomial is zero.
Example 1 : Find the degree of each of the polynomials given below:
(i) x5 – x4 + 3 (ii) 2 – y2 – y3 + 2y8 (iii) 2
Solution:
(i) The highest power of the variable is 5. So, the degree of the polynomial is 5.
(ii) The highest power of the variable is 8. So, the degree of the polynomial is 8.
(iii) The only term here is 2 which can be written as 2x0. So the exponent of x is 0. Therefore, the degree of the polynomial is 0.
