Worksheet on degree of polynomial

In this post, you will get a worksheet based on the degree of the polynomial. Check this polynomial notes 

Q.1 Write the definition of the degree of the polynomial 


Solution: Degree of the polynomial: In the polynomial , the highest power of the variable in any term is called the degree of the polynomial.

For example: In polynomial 2y²3y+4,   2 is the highest power of any variable .Hence,2 is the  degree of the polynomial


Q.2 Write the degrees of each of the following polynomials 

(i) 7x³+4x²-3x+12

(ii) 12-x+2x³

(iii) 0


Solution:

(i) 3

(ii) 3

(iii) Undefined {remember it }


Explanation: (i) In the polynomial 7x³+4x²-3x+12, the highest power of any variable is 3 . Hence Degree of the polynomial is 3

(ii) In the polynomial 12-x+2x³, the highest power of any variable is 3. Hence Degree of a polynomial is 3

(iii) You read in answer, its degree is undefined. This is why we can write 0x^∞ , its value remains 0.So, the highest power of the variable is undefined in this case.


Q.3 Give an example each of a binomial of degree 35, and of a monomial of degree 100 .


Solution:

Binomial x^35-8

Monomial x^100


 

Q.4 Identitfy the polynomial on the basis of degree 

(i) f(x) = 4x³-x²-3x+7

(ii) 2+\frac{3}{x}+4x

(iii) 2x³-3x²+√x +1


Solution:

(i) Cubic polynomial

(ii) This is not a polynomial

(iii) Not a polynomial


Explanation:

(i) Highest power of the variable is 3 , degree of the polynomial is 3 . We know, polynomial with a degree of 3 is called a cubic polynomial.

(ii) It has negative power in the variable, so it is not a polynomial

(iii) It has fractional power in the variable, so it is not a polynomial . Polynomial has only whole number power


Q.5 Write the name of four polynomial on the basis of their degree.

Solution: These are four types of a polynomial on the basis of the degree

(i) constant polynomial

(ii) linear polynomial

(iii) cubic polynomial

(iv) bi-quadratic polynomial


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