# RD Sharma Class 9 Chapter 6 Solutions (Factorisation of Polynomials)

RD Sharma Solutions for Class 9 Chapter 6 ‘Factorisation of Polynomials’ are created to provide you with aid in understanding the concepts of polynomials in detail. The topics of the polynomials covered in the chapter are terms and coefficients in polynomials, an introduction of how to factorize polynomials using the factor theorem, degree of a polynomial and types of a polynomial. You will also get to learn the remainder theorem in this chapter of RD Sharma Solutions. This chapter is crucial from the exam perspective. It is recommended that you consistently practice the exercises to get good marks in your exams.

There are 29 questions in this chapter arranged in 5 exercises in total with an additional exercise comprising 6 questions. You will get to solve enough questions related to each and every topic discussed in the chapter. The exercises of the chapter include questions of varying difficulty levels. These questions will give you an idea about the pattern of problems asked in the exams.

To be able to achieve a good rank among your fellow classmates, it is crucial that you revise the exercise questions of this chapter regularly. The Instasolv experts have addressed all the possible doubts that might arise while solving the exercises of the chapter. You will also find the concepts simplified in a question-answer format at our platform. This will help you memorising the essential formulae and theorems effectively.

## Important Topics for RD Sharma Solutions for Class 9 Chapter 6: Factorisation of Polynomials

**Introduction**

- The algebraic expressions that have only whole numbers as the exponents of their variable are known as Polynomials.
- The different components of a polynomial separated by a plus or minus sign are known as terms of the polynomial.
- Each term of a polynomial has a constant in multiplication with the variable, which is called a coefficient.
- Integers are examples of constant Polynomials. The constant polynomial 0 is called the zero polynomial.
- Polynomials having only two and three terms are called binomials and trinomials respectively.
- We call the highest power of the polynomial as the degree of the polynomial. The degree of a non-zero constant polynomial is zero. Polynomials of degree two and three are known as quadratic and cubic Polynomials respectively.
- A polynomial in one variable x of degree n can be expressed in the form a
_{n}x+ a^{n}_{n-1 }x+… + a^{n-1}_{1}x+ a_{0 }Where, a_{0}, a_{1}, a_{2},…, a_{n}are constants and*a*≠ 0 If_{n}*a*_{n}= 0, then we get the zero polynomial, the degree of which is not defined.

**Zero of a Polynomial**

- Zero of the polynomial p(x) under consideration is a number c, so that p(c) = 0
- A non-zero constant polynomial such as ‘8’ has no zero while we assume that all the real numbers are zeroes of the zero polynomial.
- There is just one zero of a linear polynomial.
- 0 may be a zero of a given polynomial but this can also be false.
- A polynomial might also have more than one zeroes.

**Remainder Theorem and Factor Theorem**

Dividend = (Divisor x Quotient) + Remainder

So, if p(x) and g(x) are two Polynomials with degree of p(x) g(x), then Polynomials q(x) and r(x) can be found such that:

p(x) = g(x)q(x) + r(x),

where degree of r(x) degree of g(x)

r(x) and q(x) represeny remainder and quotient respectively.

**Remainder Theorem:** Let p(x) be any polynomial of degree 1 and let a be any real number. If p(x) is divided by the linear polynomial x-a, then the remainder is p(a).

**Factor Theorem: **If we consider a polynomical p(x) is a polynomial with degree n > 1 and a as any real number, then according to this thoerem (i) x-a is a factor of p(x), if p(a)= 0; and (ii) p(a) = 0, if x-a is a factor p(x).

**Important Points to Remember**

- Polynomials comprising one, two, and three terms are called monomials, binomials, and trinomials respectively.
- All the linear polynomials which consist of only one variable has only 1 zero.
- The degrees of the Linear, Quadratic and cubic Polynomials are 1, 2, and 3 respectively.
- We can use Identities to split the terms in a polynomial for factorization using the factor theorem.

### Exercise Discussion for RD Sharma Solutions for Class 9 Chapter 6: Factorisation of Polynomials

- Exercise 6.1 is a basic exercise that will require an in-depth understanding of the terms, coefficients, and degrees of polynomials.
- In exercise 6.2, you will learn to find the zeroes of the polynomials and verify if a given real number is the zero of a polynomial or not.
- There are 7 questions in exercise 6.3 which are mainly based on the remainder theorem.
- In exercise 6.4 and exercise 6.5, you will be required to find the factors of the given polynomials using the factor theorem. 6.5 is an extension with some advanced level questions related to factorisation of polynomials.
- The VSAQs exercise is a miscellaneous exercise consisting of questions based on all the topics mentioned above. The problems in this exercise are easy such as writing the definition of the zeroes of the polynomial. There are 6 questions in this exercise.

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