How Do You Determine The Degree Of A Polynomial

Degree Of A Polynomial

The greatest power (exponent) of the terms of a polynomial is called degree of the polynomial.
For example :
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
The degree of polynomial :
(i) 4y³ – 3y + 8 is 3
(ii) 7p + 2 is 1(p = p¹)
(iii) 2m – 7m⁸ + m¹³ 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) 3x² – 5x        (ii) \(\text{x + }\frac{1}{\text{x}}\)     (iii) √y– 8             (iv) z⁵ – ∛z + 8
Sol.
(i) 3x² – 5x = 3x² – 5x¹
It is a polynomial.
(ii) \(\text{x + }\frac{1}{\text{x}}\) = x¹ + 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) z⁵ – ∛z + 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 2:    Find the degree of the polynomial :
(i) 5x – 6x³ + 8x⁷ + 6x²    (ii) 2y¹² + 3y¹⁰ – y¹⁵ + y + 3   (iii) x    (iv) 8
Sol.
(i)  Since the term with highest exponent (power) is 8x⁷ 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 = x¹   ⇒   degree is 1.
(iv)  8 = 8x⁰   ⇒   degree = 0