RS Aggarwal Class 9 Chapter 3 Solutions (Factorisation of Polynomials)
RS Aggarwal Solutions for Class 9 Maths Solutions Chapter 3 – Factorisation of Polynomials will help you prepare better for the CBSE exams. In this chapter of RS Aggarwal Solutions for Class 9 Maths Solutions, there are a total of 220 exemplar problems divided into 7 exercises. We will learn about the concepts of Students will also study the remainder theorem and factor theorem in this chapter.
Some more algebraic identities have been discussed in this chapter. This can be used in factorisation and calculation of some given expressions. Further, different polynomials based on the number of terms are discussed in this chapter.RS Aggarwal Solutions for Class 9 Maths Solutions Chapter 3 by instasolv sets a benchmark for you to prepare it thoroughly and solve any type of question in the examination irrespective of its difficulty level.
Instasolv’s RS Aggarwal Solutions for the chapter Factorization of Polynomials help clear their basic understanding regarding this chapter as there is a probability of 10 -12 marks questions from this chapter. These RS Aggarwal problems with Solutions can be followed for CBSE final examinations. Solving the exercise wise problems daily helps students improve their problem solving and logical thinking skills, important to obtain a better academic score.
Important Topics for RS Aggarwal Solutions for Class 9 Maths Solutions Chapter 3 – Factorisation of Polynomials
- Factor theorem: Assume as a polynomial p(x) of degree n>1 and let “a” be any real number.
- Factorisation: To precise a given polynomial as the item of polynomials each of degree less than that of the given polynomial such that no such a factor contains a calculated lower degree, is called factorisation.
For Example: x2-16 = (x+4)(x-4)
- Methods of Factorisation: Factorisation By taking out the common factor under factorisation
- Factorisation of quadratic trinomials (middle term splitting method).
- Identity: It is an equation (trigonometric, algebraic) that is true for each value of variables.
- Few algebraic identities that are useful in the method of factorisation :
- A polynomial can be spoken to as an item of polynomials with its degree less than or equal. Each polynomial which is included to discover the product is called a factor. A polynomial can be spoken to as an item of polynomials with its degree less than or rise to it.
- Each polynomial which is included to discover the product is called calculates. The process included in breaking a polynomial and making it as a product of its figure is called the Factorisation of Polynomials.
- Constants: Fixed numerical values of any symbol are called a constant.
i.e. 7, 3, -2, 3/7, etc. are all constants.
- Variables: Any symbol that might assign to different numerical values are known as a variable.
C=2Πr i.e., (Circumference of a circle)
“r “- radius of circle Where 2 as constants. While “C” and “r” are variable
- Algebraic expressions: Mixture of constants plus variables. Connected through few or all operations i.e., +, -, x and is known as an algebraic expression.
- Various parts of expression of an algebra separated via “+” or “-“operations are known as the expression.
- Polynomials: It is an algebraic expression where the variables taken part that has only non-negative power of integral are known as a polynomial.
- Coefficients: Within a polynomial x3 + 3x2 + 3x + 1 coefficient of x3, x2, x are 1, 3, 3 as shown and alongside the constant term in it will be +1.
- Polynomial degree in one variable: The maximum power of the variable is known as the degree of the polynomial.
- Categories of polynomials on the degree basis:
- Classification of polynomials on the number of terms basis:
- Constant polynomial: Polynomial when containing only one term, consisting of a constant term is called a constant polynomial. The degree of a non-zero constant polynomial is always zero.
- Zero polynomial: A polynomial having only a single term, which is zero called a zero polynomial. A zero polynomial degree is not defined.
Zeros of a polynomial: Let us take “p(x)” as a polynomial. Where if then we can say the polynomial of p(x) is zero.
- Remark: Searching zeros of polynomial p(x) ensure solving equations p(x) =0.
- Remainder theorem: Let us assume f(x) as a polynomial of degree >0 and consider it as any real number. When f(x) is divided by f(x-a) then the remainder is f(a).
- Use of a grouping method
Whenever a common factor exists between the groupings at that time factor polynomials are used.
- The other two methods are by using special factoring formulas where you need to memorize for your exams; they include the formulas for factoring the sums and the differences of cubes. Here are the two formulas:
- Factoring a Sum of Cubes:
a3 + b3 = (a + b) (a2 – ab + b2)
- Factoring a Difference of Cubes:
a3 – b3 = (a – b) (a2 + ab + b2)
- You’ll learn more as you move up in your advanced classes and you will learn how these formulas have come up.
Exercise Discussion of Important Topics for RS Aggarwal Solutions for Class 9 Maths Solutions Chapter 3 – Factorisation of Polynomials
- Exercise 3A of the third section in RS Aggarwal Solutions for Class 9 Chapter 3 essentially contains 34 questions dependent on the factorisation techniques and methods for gathering polynomials by utilizing factorisation. Numerous inquiries are posed concerning Methods of Factorisation and Factorisation by grouping.
- Math Chapter 3 Exercise 3B has 40 models and issues which depend on the idea of Factoring the distinction of two squares. You must know a step by step procedure to complete a question.
- Math Chapter 3 Exercise 3C has 66 examples along with answers for exercises that are based on the Factorisation of Quadratic Trinomials which are marks fetching in nature.
- Math Chapter 3 Exercise 3D has a set of 7 problems based on the topic Square of a Trinomial. Experts will help you in solving and clarify your doubts about the questions in this Exercise. Though these questions seem very easy, they need good preparation.
- Math Chapter 3 Exercise 3E contains 10 examples based on the descriptive manner for the fifth exercise to find the cube of a binomial. Revision of chapter 3 can be done under lesser time by using the instasolv Solutions for Class 9.
- Math Chapter 3 exercise 3F contains 38 problems, which are based on the concept of Factorisation of Sum or Difference of Cubes. Doubts that arise in students while solving the problems can be cleared immediately.
- Math Chapter 3 Exercise 3G has 25 problems that help students understand the methods used to solve lengthy problems based on Theorem 1 and 2 in factorisation. The Solutions are prepared in a stepwise manner to provide an effortless and better understanding of the concepts.
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