Polynomials Worksheets

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Define Polynomial

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

FAQ (Frequently Asked Questions)

Q1. What are the Key Takeaways From the Polynomials Class 9 Worksheet?

Answer: Listed below are some of the key takeaways from polynomials worksheet Class 9.

  • Terms that are present in the situation of a polynomial are either a variable or a single number or they might also be a combination of variable and numbers.

  • Polynomial degrees are the highest power of the variable in a polynomial.

  • A monomial is a term used for the polynomial of 1.

  • A binomial is referred to as the polynomial of 2 terms.

Q2. In the Below Question, Find the Coefficients of x and Find the Degree of the Polynomial in the Second:

i. 3x + 1

ii. 23x2 – 5x + 1


Answer: For the first question, we need to calculate the coefficients of x:

i. 3x + 1

ii. 23x2 – 5x + 1

Solution:

Here, in 3x + 1, the coefficient of x is 3.

Further, in the given numerical of 23 x2 – 5x + 1, the coefficient of x is -5.

Moving to the second part of the question that requires us to find the degrees of following polynomials:

  • 3a2 + a – 1

  • 32x3 + x – 1

3a2 + a – 1: 2 is the coefficient degree

23x3 + x – 1 : 3 is the coefficient degree