Polynomials Worksheets

Polynomials are a form of algebraic expressions that consist of variables, coefficients, and constants. This chapter deals with a number of sums focused on simplifying different exponential polynomial expressions. The Polynomials Class 9 worksheet with answers PDF will help you evaluate your understanding of the concepts of this chapter. The Class 9 polynomial worksheet is one of the most useful study resources that aims to teach students the application of various theories of polynomials. Students can self-assess the understanding of the basic concepts by referring to the Worksheet for Class 9 CBSE Maths Polynomials.

About Polynomials

The Polynomials Class 9 worksheet PDF focuses on explaining the term, according to the worksheet, Polynomials are expressions that can be related to one or more terms and used seamlessly with a non-zero coefficient, in a way that it can carry more than one term.

In the polynomials worksheet class 9, each expression that is used in the sum of a polynomial is defined as a term. Let’s suppose that x² + 5x + 2 is polynomial. In the given example, we can say that the expressions are laid in a way that x², 5x, and 2 are the terms that are laid in the form of a polynomial. Remember, every single term that is given in a polynomial comprises a coefficient.

Further, the real numbers that are used in the polynomials can also be used to express different terms in the grade 9 math polynomial worksheets. Similar to how the certain numbers are polynomials without any variables, they are known as constant polynomials.

In theory, the constant polynomial 0 is also known as zero polynomial. Degree of the polynomial is the highest power that is available to the suggested polynomial. Consider an example where x³ + y³ + 3xy(x + y), the degree of the polynomial is 3. In a situation where the degree of the sum is a zero, the constant polynomial is a non zero.

Apart from these, polynomials can be further categorised into the suggested three types:

• Linear Polynomial – of degree one.

• Quadratic Polynomial – of degree two.

• Cubic Polynomial – of degree three.

Solved Problems

Q1. Define the suggested degree of each polynomial that is listed below.

(i) 5x3 + 4x2 + 7x

(ii) 4 – y2

(iii) 5t – √7

(iv) 3

Solution:

(i) The given polynomial is 5x³ + 4x² + 7x.

The suggested equation provides us with a situation where 3 is the highest power of the variable x. So, the degree of the polynomial is 3.

(ii) The given polynomial is 4 - y². 2 becomes the highest power of the suggested variable that is, y = 2. So, the degree of the polynomial is 2.

(iii) In the suggested polynomial of the situation where 5t – √7. The highest power of variable t is 1. So, the degree of the polynomial is 1.

(iv) Since, 3 = 3x° [∵ x°=1] The equation suggests that the degree of the polynomial for the given equation is a 0.

Q2. Verify whether 2 and 0 are zeroes of the polynomial x² – 2x.

Solution : 

Let p(x) = x² – 2x

Then p(2) = 22

 – 4 = 4 – 4 = 0 and p(0) = 0 – 0 = 0

The solution suggests that the sum 0 and 2 are both the zeroes of the polynomial x² – 2x.

Listed below are the list of observations around the sums:

(i) The resultant sum of a polynomial doesn’t really have to be a 0.

(ii) The term of a zero polynomial might be a 0.

(iii) Polynomials might comprise of more than one zero