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

## 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 x ^{3} + ax^{2} + 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) = x^{3} + ax^{2} + 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.