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# ICSE Class 10 Mathematics Revision Notes Chapter 8 - Remainder and Factor Theorems

Last updated date: 22nd May 2024
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## Revision Notes for ICSE Class 10 Math Chapter 8 - Free PDF Download

Chapter 8 of the ICSE Class 10th Maths is Remainder and Factor Theorems. This chapter is mainly about finding factors and the remainder of the given polynomial by using the factor and remainder theorems. To make this chapter more interesting and easy to understand, Vedantu provides the revision notes and the ICSE solutions of this chapter on its official website. The notes contain all the important topics. Students can use these notes to understand each concept and solve the questions. As these notes are very useful, students must access them if they desire to score good marks in their ICSE Class 10th Mathematics exam.

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## Revision Notes for ICSE Class 10 Maths Chapter 8 - Free PDF Download

Free PDF download of Class 10 Mathematics Chapter 8 - Remainder and Factor Theorems Revision Notes & Short Key-notes prepared by our expert Math teachers as per CISCE guidelines. The content of the revision notes is designed after doing lots of research. The Maths experts use easy to understand dialect for creating the notes so that students can understand them. They can download these notes in the form of a PDF file. To register Maths Tuitions on Vedantu to clear your doubts.

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### Importance of the Revision Notes of Chapter 8 Remainder and Factor Theorem

Mathematics is a reasoning and an application based subject. To solve the questions, it is important to understand the theory behind the chapter. The revision notes are very helpful. Therefore, students must refer to these notes as they are of great importance. Some of the benefits of the revision notes are mentioned below:

• Revision notes help students to retain significant information till the examination.

• It saves a lot of time for the students at the time of the exam so that they can focus on other things.

• These notes are easily available everywhere on the internet.

• The revision notes provide the summary of the chapter.

• The notes help in improving the learning skill of the students.

## FAQs on ICSE Class 10 Mathematics Revision Notes Chapter 8 - Remainder and Factor Theorems

1. Why is it advised to use Vedantu for studying Chapter 8 Remainder and Factor Theorem of the ICSE Class 10 Mathematics?

Students are advised to prefer Vedantu for Studying Chapter 8 Remainder and Factor Theorem of the ICSE Class 10 Maths due to the following reasons:

• It furnishes students with the well-prepared notes of the chapter.

• The Vedantu experts help them in solving their queries.

• Besides notes, it also offers the ICSE solutions of the chapter.

• It allows students to access these study materials by downloading them in PDF format.

• Other study materials like the NCERT solutions, important concepts, popular books solutions, etc are also available on Vedantu.

2. What is a factor of a polynomial that is discussed in Class 10 Maths Chapter 8?

A unique polynomial q (x) exists satisfying the condition f (x) = g(x).q (x) + r (x). Here, f (x) is the polynomial which is divided by a non-zero polynomial g (x). This non-zero polynomial g (x) will act as a factor of the polynomial f (x) if the remainder becomes zero when f (x) will be divided by g (x). In mathematical form, the factor can be described as f (x) = g (x).q (x) + r (x)

g (x) is a factor, thus r (x) = 0

Therefore, f (x) = g (x).q (x)

3. Write the statement of the factor theorem as described in Chapter 8 of Class 10 Maths.

Factor Theorem – This theorem states that f (x) is a polynomial over the set of real numbers R. The polynomial f (x) is divided by (x – a), here ‘a' belongs to the set of real numbers and f (a) is the remainder. Mathematically,

f (x) = (x – a)Q + R, Q is the quotient and R is the remainder. The remainder can also be written as R = f (a)

The remainder will be f (-a) if f (x) = (x + a)Q + R

4. According to the concepts taught in chapter 8 of class 10 Maths, if (x - 2) is a factor of the polynomial x3 + ax2 + bx + 6 and is divided by (x – 3) leaving a remainder 3, then find the values of a and b.

Let the polynomial f (x) = x3 + ax2 + bx + 6

x – 2 = 0

x = 2

As x – 2 is a factor therefore remainder is zero

f (2) = 0

(2)3 + a(2)2 + b(2) + 6 = 0

8 + 4a + 2b + 6 = 0

2a + b + 7 = 0.  (i)

x – 3 = 0

x = 3

f (x) divided by x-3 leaves a remainder 3

(3)3 + a(3)2 + b(3) + 6 = 3

27 + 9a + 3b + 6 = 3

3a + b + 10 = 3.    (ii)

Subtract equation (i) from (ii)

We get, a + 3 = 0

a = -3

Substituting the value of ‘a’ in (i)

-6 + b + 7 = 0

b = -1

5. How to obtain maximum marks in Chapter 8 Remainder and Factor Theorem of the ICSE Class 10 Mathematics?

It is easy to score good marks in Mathematics when concepts are clear. One has to practice solving questions a lot to obtain good marks. They can prepare Chapter 8 Remainder and Factor Theorem easily by following a proper study plan. They should only focus on the ICSE Maths textbook to understand the chapter. They should practice each question of this book. They can use the revision notes to learn and remember every formula of the chapter. They can do their self-analyzation by solving the mock test papers. These strategies will enable students to prepare Chapter 8 Remainder and Factor Theorem of the ICSE Class 10th Maths.