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 
T Nagar, Chennai 
5 students 
1157 hrs of classes completed 
500 per hour 
Online Classes BDS Graduate from Government Dental College, Chennai | CBSE Class 10 Science & Maths | Class 11-12 Biology & Chemistry | NEET Biology & Chemistry Mentor About Me I am a BDS graduate from Government Dental College, Chennai, with a strong academic foundation in Biology, Chemistry and the life sciences. My passion for teaching led me to become a full-time online educator, helping students build confidence through conceptual learning rather than rote memorization. My teaching approach is designed to help students understand concepts from the basics and gradually progress to exam-level application. Every class is interactive, student-friendly and tailored to the learner's pace. What students can expect ✔ Strong conceptual understanding from fundamentals ✔ NCERT-focused teaching for Boards and NEET ✔ Step-by-step explanation of difficult topics ✔ Previous Year Questions and exam-oriented practice ✔ Regular MCQs, assignments and chapter-wise tests ✔ Doubt-solving sessions and revision classes ✔ Personalized study plans based on each student's strengths and weaknesses ✔ Time management and exam strategy guidance Why learn with me? Being a healthcare professional has given me an in-depth understanding of Biology and Chemistry, enabling me to explain even complex topics in a simple, logical and relatable manner. I have successfully guided students in improving their conceptual understanding, academic confidence and examination performance. My objective is not just to help students score high marks but also to develop genuine interest and long-term understanding of the subject. I believe every student can excel with the right guidance, structured learning and regular practice. My classes are supportive, interactive and result-oriented, ensuring students gain both knowledge and confidence. Subjects 🔷️Class 10 (CBSE & State Board): ▪️Science ▪️Mathematics 🔷️Class 11 & 12 (CBSE): ▪️Biology ▪️Chemistry 🔷️NEET Preparation: ▪️Biology ▪️Chemistry 🔷️NCERT Line-by-Line Learning MCQ Practice Previous Year Questions Exam Strategy Doubt Solving One suggestion Book a demo class and experience concept-based learning that makes studying easier, smarter and more effective.
Top Tutor New Town, Kolkata 44 students 55 hrs of classes completed 200 per hour Online Classes I am a strong believer in concept-based gain of knowledge. I start from scratch while teaching the very basic concepts and take my students to a level where they have a deep understanding of the subject. Once they understand the concept, the next step is that practice a lot of questions/numerical/problem in the class itself as practice is the key to retaining the knowledge. I always refer to prescribed books by CBSE/ICSE board but always encourage students to refer additional 1 or 2 books based on their speed to practice. In last I provide them enough homework to practice at home and send me the doubts before the next class. This approach till date have been fruitful as most of my students excel in the school exams as well as in next classes
We had a wonderful experience. Sir conducts group class but managed to give individual attention to each students. My daughter benefitted a lot and managed to score good marks jn her boards .
Top Tutor Nigdi, Pune 1 hrs of classes completed 350 per hour Online Classes 
Student's Home I have excellent teaching experience of 7 years with best results with my previous student's from CBSE , STATE and ICSE BOARD'S . Preferably i focus on students personal interest, level of understanding and study methodology. I am here to give best of me to seek best out from my students. I have given seminar on 'Students changing Virtue towards study , Need if time??' . Passionate to guide students towards there destiny
Super Tutor Yapral, Hyderabad 11 students 660 hrs of classes completed 700 per hour Online Classes Student's Home 
Tutor's home With 7+ years of experience teaching hundreds of 8th, 9th, and 10th-grade students, I understand exactly where students struggle—and more importantly, how to help them succeed! My approach goes beyond traditional teaching—I identify each student’s unique challenges and provide customized mentorship, proven strategies, and smart tricks to turn weaknesses into strengths. Through one-on-one support and a positive, encouraging learning environment, I help students build confidence, overcome obstacles, and achieve outstanding results. There’s nothing more rewarding than watching a student’s face light up with that "Happy!" moment—and seeing their grades soar!
Awesome teacher with great teaching skills. He knows the pulse of students and shifts his focus entirely as per students' needs
Top Tutor Thane West, Thane 10 students 3904 hrs of classes completed 350 per hour Online Classes This is Debabrato Chatterjee, online Math and Science tutor with 13+ years of experience. I have taught students of IB, IGCSE, CBSE, ICSE, Maharashtra State Boards. I teach students from grade 6 to 12. My teaching style is to start with concepts and their application. Solving lots of sample paper along with homework will help in grasping the concepts well.
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.
