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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
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Remainder Theorem: Quick Polynomial Checks
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Top Tutors who teach Remainder Theorem
Top Tutor 
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10 students 
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350 per hour 
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Very generous and effective teaching. She gets down to the level of the child and tries to understand her shortcomings and teach accordingly.
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Top Tutor Vijay Nagar, Indore Online Classes 
Student's Home 
Tutor's home I have been working in International schools across India, total of 5 years of teaching,
Super Tutor Itagalpura Main Rd, Madappanahalli 45 students 3602 hrs of classes completed 400 per hour Online Classes I gained extensive experience in delivering high-quality education following the CBSE/ICSE curriculum. My key responsibilities included: Classroom Teaching: Effectively taught Mathematics, Physics and Chemistry to students of classes IX, ensuring alignment with the CBSE/ ICSE syllabus and fostering a deep understanding of key concepts. Curriculum Planning: Designed and implemented lesson plans that adhered to the CBSE guidelines, ensuring comprehensive coverage of topics while keeping in mind the varying learning needs of students. Student Assessment: Created and administered tests, quizzes, and assignments in accordance with the CBSE exam pattern. Monitored student performance and provided constructive feedback to facilitate continuous improvement. Interactive Learning: Encouraged an interactive classroom environment, integrating various teaching aids such as multimedia presentations, hands-on activities, and group discussions to enhance student engagement and understanding. Preparation for Board Exams: Provided focused support for students appearing for their CBSE/ICSE board exams by conducting regular revision sessions, mock tests, and personalized guidance to help them excel. Parental Communication: Maintained regular communication with parents regarding student progress, attendance, and overall development. Organized parent-teacher meetings to ensure a collaborative approach to student growth. Co-curricular Involvement: Actively participated in school events, projects, and extracurricular activities, fostering holistic development among students. Professional Development: Engaged in continuous professional development through workshops and CBSE training programs to stay updated with the latest educational practices and policies.
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Top Tutor Malkajgiri D.D.Colony, Hyderabad 2 students 1273 hrs of classes completed 300 per hour Online Classes PPP Approach to make the students understand the topics. Unified Approach to make the students to work independently and collaboratively. Heuristic Approach to make the students to understand theories through lab practical. Use few other contemporary approaches not limited to Brain Storming, Mind Mapping, Concept Mapping, Snowballing etc., Providing supervision & consultation for students, in the form of academic advising, students’ support, recruitment, courses and programs. Also, participating in student & staff social and cultural activities.
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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.
