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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
CBSE - Class 9>Mathematics>Polynomials>Remainder Theorem
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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
Super Tutor 
Jankipuram, Lucknow 
5 students 
985 hrs of classes completed 
500 per hour 
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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.
