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 = y1/2– 8

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

(iv) z5 – ∛z + 8 = z5 – 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 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

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