Find the best tutors and institutes for Class 9 Tuition
Learn Remainder Theorem
Welcome to CBSE Class 9 Mathematics. In the crucial chapter of "Polynomials," you will frequently encounter the division of algebraic expressions. While the traditional long division method works, it is heavily time-consuming and prone to calculation errors. This is where the Remainder Theorem comes to your rescue as a brilliant mathematical shortcut. Simply put, this theorem allows you to find the exact remainder of a polynomial division without ever having to actually perform the long division process. It connects the concept of evaluating a polynomial at a specific point directly to the remainder found during division.
The core logic of the Remainder Theorem states that if a polynomial p(x) of a degree greater than or equal to one is divided by a linear polynomial (x - a), where a is any real number, then the remainder is exactly equal to p(a). To find the remainder mathematically, you first find the "zero" of your divisor by setting x - a = 0, which easily gives you x = a. Next, you simply substitute this value of a wherever there is an x in your original polynomial p(x). If your final calculated remainder p(a) happens to be zero, it acts as a bonus proof that (x - a) is a perfect factor of the polynomial!
The infographic above perfectly illustrates how to apply the Remainder Theorem using a practical example. On the left, we identify our target polynomial, p(x) = x² - 3x + 5, and the linear divisor, x - 2. Instead of calculating a complex algebraic long division, we use the theorem's shortcut: extracting the zero of the divisor (which gives us a = 2). Following the arrow to the right, we systematically substitute x = 2 into the original polynomial. Evaluating the mathematical expression gives us a final value of 3. This means 3 is our remainder! In your CBSE Class 9 exams, you will be frequently tested on this exact method to quickly verify remainders or check if a given linear expression is a perfect factor of a larger polynomial.
Mastering algebra and polynomial theorems can initially feel challenging, but with the right guidance, it becomes an incredibly logical and high-scoring subject. If you are struggling with polynomials, understanding algebraic identities, or finding the zeros of equations, consider getting personalized academic help. Explore UrbanPro to find highly experienced, verified Class 9 Mathematics tutors who offer both customized online sessions and local offline tuition. A dedicated math tutor on UrbanPro can help you practice these essential math shortcuts step-by-step, ensuring you are fully prepared and confident to ace your upcoming CBSE school exams!
Other Concepts in Polynomials
- Definition and examples
- Degree and terms of a polynomial
- EXERCISE 2.1
- EXERCISE 2.2
- EXERCISE 2.3
- EXERCISE 2.4
- Factor Theorem
- Factorisation of polynomials
- Zeroes of a polynomial
Other Concept Videos for Remainder Theorem
Remainder Theorem: Quick Polynomial Checks
CBSE - Class 9>Mathematics>Polynomials>Remainder Theorem
Breaking Down Polynomials Using Factorisation
CBSE - Class 9>Mathematics>Polynomials>Remainder Theorem
Super Tutor 
Remainder Theorem: Quick Polynomial Checks
CBSE - Class 9>Mathematics>Polynomials>Remainder Theorem
Top Tutors who teach Remainder Theorem
Top Tutor 
Sector-18, Faridabad 
6 students 
1038 hrs of classes completed 
600 per hour 
Online Classes 
Tutor's home I have approximately 3 years of experience of teaching Mathematics across different boards including CBSE, IGCSE and state board in reputed schools like DPS International. I am post graduate in statistics and honors degree in mathematics from reputed universities like DU. I have helped many students to overcome their fear of Mathematics and Statistics. My aim is to develop a genuine love for the subject in students.
She is an amazing teacher who explains everything clearly and makes learning fun. Her patience and support have really helped me improve and feel more confident in math. I'm lucky to have her as my teacher.
Top Tutor Anna Nagar Western Extn, Chennai 3 students 58 hrs of classes completed 500 per hour 
Student's Home I am an experienced, qualified teacher and tutor with over 6 years of experience in teaching Maths across different boards including CBSE, ICSE, IGCSE and State Board. Passionate about solving mathematical problems. over the years I have helped hundred of students overcome their fear of Maths. I am a post graduates in mathematics and under graduates in education. We are available on both home tuition and online We have lot of success stories.
Top Tutor Vesu, Surat 17 students 1266 hrs of classes completed 500 per hour Online Classes I have experience teaching Mathematics to Grade 9 students with a focus on building strong basic concepts and developing logical thinking. I teach key topics such as Number Systems, Polynomials, Linear Equations in Two Variables, Coordinate Geometry, Euclid’s Geometry, Triangles, Quadrilaterals, Surface Areas and Volumes, Statistics, and Probability. My teaching method includes clear explanation of concepts, step-by-step problem solving, and regular practice from NCERT exercises. I also conduct class tests, revision sessions, and doubt-clearing classes to help students understand topics thoroughly. My aim is to make mathematics easy and interesting, strengthen students’ fundamentals, and prepare them for higher classes and future mathematical learning.
Sir, is an excellent teacher who focuses on the basics first and then to the intricacies. He connects with the student very well and always remains connected. He is the best teacher available and I wish to always remain connected with him for my son's Mathematics. I wish him all the best.
Top Tutor Kasavanahalli Main Rd Kasavanahalli, Bangalore 1 student 703 hrs of classes completed 800 per hour Online Classes I am a teacher. I love teaching and want to share my knowledge with my students. I will take online classes. My approach combines clear concepts, regular practice, and student-friendly strategies to make learning effective and enjoyable.
Very good teacher. Patiently explains the doubts that my son has. Very happy with my son's progress
Super Tutor Pettah, Thiruvananthapuram 10 students 314 hrs of classes completed 300 per hour Online Classes I have more than 10 years of experience teaching Mathematics to Class 9 students under CBSE and ICSE curricula. I specialize in teaching key Class 9 topics such as Number Systems, Polynomials, Coordinate Geometry, Linear Equations in Two Variables, Euclid's Geometry, Lines and Angles, Triangles, Quadrilaterals, Circles, Heron's Formula, Surface Areas and Volumes, Statistics, and Probability. My teaching approach focuses on building strong fundamentals, conceptual understanding, and problem-solving skills. I break down complex concepts into simple, easy-to-understand steps and provide extensive practice through worksheets, assignments, and mock tests. I conduct regular assessments to track progress and identify areas that require additional attention. Personalized doubt-clearing sessions and one-to-one guidance help students overcome learning difficulties and gain confidence in Mathematics. I also train students to tackle application-based and higher-order thinking questions, preparing them effectively for school examinations. Many of my students have shown significant improvement in their grades and developed a strong foundation that supports their success in higher classes. My goal is to make Mathematics engaging, enjoyable, and accessible to every Class 9 student.
My daughter finds the tutor very helpful. She has enthusiasm to teach and never miss the classes. My daughter is able to understand the concepts well now.
Find more Tutor for Remainder Theorem in your City
- Bangalore Mathematics Tutors
- Delhi Mathematics Tutors
- Gurgaon Mathematics Tutors
- Hyderabad Mathematics Tutors
- Chennai Mathematics Tutors
- Kolkata Mathematics Tutors
- Faridabad Mathematics Tutors
- Noida Mathematics Tutors
- Mumbai Mathematics Tutors
- Surat Mathematics Tutors
- Pune Mathematics Tutors
- Ghaziabad Mathematics Tutors
FAQ
What is the meaning of Remainder Theorem?
It refers to a specific mathematical method or property in Polynomials used to solve problems involving Remainder Theorem.
Why is Remainder Theorem important for CBSE - Class 9 exams?
This concept is crucial for the exams as questions related to Polynomials and specifically Remainder Theorem are very common. It helps secure marks in the section effectively.
Is Remainder Theorem part of the latest NCERT syllabus?
Yes, Remainder Theorem is an integral part of the CBSE - Class 9 NCERT Mathematics syllabus. It is a key topic covered in the Polynomials chapter.
What are common mistakes students make with Remainder Theorem?
Students often miss the minute details or fundamental definitions of Remainder Theorem. Regular revision and practice are needed to master the nuances.
How should I approach learning Remainder Theorem?
Start by understanding the formulas and logic, then practice applying them to simple problems. Solve the examples given in the NCERT textbook before moving to exercise problems.
How can UrbanPro help me understand Remainder Theorem better?
UrbanPro connects you with experienced Mathematics tutors who can explain Remainder Theorem with simple examples. You also get access to doubt-clearing sessions and mock tests for better preparation.
