Polynomials Worksheets – Worksheet For Class 9

Polynomials Worksheets are created by subject-matter experts to provide reliable and high-quality answers. In today’s competitive environment, students need effective preparation tools. Our NCERT Solutions for Class 9 serve as valuable references to aid students in their learning journey.

Polynomial Worksheets for Class 9 Math serve as invaluable study tools, offering a hands-on approach to reinforce concepts and enhance understanding. These structured exercises provide students with practical application, encouraging active learning and problem-solving skills. By engaging with worksheets, students can reinforce theoretical knowledge, identify areas of improvement, and gain confidence in tackling diverse mathematical problems. This interactive and self-paced learning method not only complements classroom teaching but also promotes a deeper understanding of mathematical concepts, making it an essential and effective study tool for Class 9 students.

NCERT Solutions for Class 9

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Define Polynomial

A polynomial is an expression consisting of one or more terms, each of which is an integer, real number, or complex number, raised to a nonnegative integer power.

You can also access free Exemplar Solutions:

NCERT Exemplar Solutions Class 9 Maths Chapter 1

About Polynomials

A polynomial is an expression consisting of a sum of one or more terms, each of which is an algebraic equation. The terms are usually numbers, but they can also be variables. The polynomial expression is usually written with the terms descending in order of degree, from the highest power to the lowest power.

For example, the expression 2×3 + 5×2 – 7x is a polynomial. The highest power of x is 3, and the lowest power is 2. The degree of the polynomial is 3.

Polynomials can be added, subtracted, multiplied, and divided. In order to do so, the coefficients of like terms must be aligned. For example, the expression 2×3 + 5×2 – 7x can be rewritten as 2×3 + 5×2 – 7x = (2×3 – 7x) + (5×2 – x).

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.

Also Check: NCERT Exemplar Solutions Class 9

Solved Problems

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

(i) 5×3 + 4×2 + 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

$\because x°=1$

The equation suggests that the degree of the polynomial for the given equation is a 0.

You can also access free Exemplar Solutions:

• NCERT Exemplar Solutions Class 9 Maths Chapter 3
• Coordinate Geometry Class 9 Extra Questions Maths Chapter 3
• Coordinate Geometry Class 9 Notes Maths Chapter 3

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

For more visit Polynomials Worksheets – Worksheet For Class 9

You can also access free Class 9 Study Materials:

• NCERT Exemplar Solutions Class 9 Maths Chapter 2
• NCERT Notes – Class 9 Maths Chapter 2 Polynomials
• NCERT Exemplar Solutions Class 9 Maths Chapter 5
• Euclid’s Geometry Class 9 Notes Maths Chapter 5
• NCERT Exemplar Solutions Class 9 Maths Chapter 6
• NCERT Exemplar Solutions Class 9 Maths Chapter 7
• Triangles Class 9 Notes Maths Chapter 7
• NCERT Exemplar Solutions Class 9 Maths Chapter 8
• NCERT Exemplar Solutions Class 9 Maths Chapter 9
• Areas of Parallelograms and Triangles – Important Theorems
• Areas of Parallelograms and Triangles Class 9 Notes
• NCERT Exemplar Solutions Class 9 Maths Chapter 10
• Circles Class 9 Notes Maths Chapter 10
• NCERT Exemplar Solutions Class 9 Maths Chapter 11
• Constructions Class 10 Notes Maths Chapter 11