RS Aggarwal Class 9 Chapter 2 Solutions (Polynomials)
RS Aggarwal Class 9 Maths Solutions Chapter 2: Polynomials is an extremely helpful practise book for you to prepare for the CBSE exams. RS Aggarwal Maths Solutions for Class 9 Chapter 2 gives you all the details regarding polynomials. It consists of major topics like algebraic expressions, terms of algebraic expressions, polynomials in one variable, various degrees of polynomials, number of terms in a polynomial, about zeros of polynomials, division algorithm, and various theorems like remainder and factor theorem, etc.
Chapter 2 of RS Aggarwal’s textbook has 4 exercises. Exercise 2A, 2B, 2C, 2D has 6, 9, 16, and 26 questions respectively. All the questions cover the whole chapter extensively. To understand every question in detail, we suggest you follow our RS Aggarwal Class 9 Maths Solutions. These solutions are based on the latest syllabus and NCERT Textbook.
Our RS Aggarwal Solutions is a useful resource for you to develop Maths problem-solving skills. Because it provides you with the solutions in the easiest method. Not only it provides easy solutions but also it helps in enhancing your logical thinking over the concepts. It is also true, Mathematics has lots of formulas and theorems. It’s not easy for Class 9 students to remember it. That’s why our experts provided some tips and shortcuts which can help you in stressful situations.
Important topics for RS Aggarwal Class 9 Maths Solutions Chapter 2: Polynomials
Let’s have a look at some beautiful concepts regarding this chapter:
You may be familiar with the word “expressions”. So, what are expressions? Expressions are the equations which have several terms which include constants, variables, exponents, etc. However, in the polynomial case, as the word “poly” means many and ” nomials” means terms suggest that it is the algebraic expression that contains many terms. These terms are constants, variables, and exponents, etc.
4x3 + 3x2 + x +3 is a polynomial in variable
4x2 + 3x-1 – 4 is not a polynomial as it has negative powers
3x3/2 + 2x – 3 is not a polynomial.
Polynomial in one Variable
When an algebraic expression has only one variable, they are called polynomials in one variable.
For Example- x – 4 is a polynomial in one variable x.
Degree of Polynomials
Degrees of polynomials are the highest value of the power of variables of an algebraic expression.
For Example– x3 + x – 4, has degree 3.
Types of polynomials
Based on degree, polynomials are divided into three types of polynomials
- Constant Polynomial – Polynomials that have degree 0 are termed as constant polynomials.
For Example- 1,4,-6, are constant polynomials.
- Linear polynomials- Polynomials that have degree one, are termed as linear polynomial
For Example– 2x – 4, is a linear polynomial.
- Quadratic Polynomials– Polynomials that have degree 2, are termed as quadratic polynomials.
For Example– 3x2 + x +8 , is quadratic polynomial
- Cubic Polynomials– Polynomials that have degree three, are termed as a cubic polynomial
For Example– x3 + x – 4, is a cubic polynomial.
- Zeros of Polynomials-
Zeros of the polynomial is the number at which the value of the polynomial is equal to vanishes. Like P(x) is a polynomial and a number ‘a’ at which the polynomial p(a)= 0 is termed as zeros of the polynomial.
For Example– X – 5 is a polynomial.
For finding the zeros of the polynomial, we to equate p(x)= 0
X – 5 = 0
X = 5 is a zero of the polynomial.
This means that for finding the root of a polynomial, we have to find the value of variable x.
- Factorization of Polynomials
Factorization of the polynomials can be done in three ways:
- By Common-factor method
- By grouping Method
- By splitting the middle term.
- Remainder Theorem
As we know the property of division-
Dividend = (Divisor × Quotient) + Remainder
This property also follows in polynomials.
If p(a) and g(a) are two polynomials which follows the conditions:
degree of p(a) ≥ degree of g(x)
and g(a) ≠ 0 are given
then we can find the q(a) and r(a) so that:
P(x) = g(a) q(a) + r(a),
where r(a) = 0 or degree of r(a) < degree of g(a).
It states that when p(a) divided by g(a), it gives q(a) as quotient and r(a) as remainder.
Exercise Discussion for RS Aggarwal Class 9 Maths Solutions Chapter 2: Polynomials
- RS Aggarwal Class 9 Maths Solutions Chapter 2: Polynomial contains 4 exercises 2A, 2B, 2C, and 2D respectively. The questions on these exercises cover all the concepts of this chapter extensively.
- Exercise 2 A of RS Aggarwal’s Textbook contains 6 questions based on the concepts: types of polynomials like( constant, linear, quadratic, and cubic), degrees of polynomials. These questions are simple to solve at which you need to just identify the types of polynomials and to find the degrees of polynomials.
- Exercise 2 B has 9 RS Aggarwal’s problems based on the concept of Zeros of polynomials. There are the questions at which you need to find the zeros of the given polynomial, and in some of which you have to verify that the expression has the correct zero polynomial or not.
- Exercise 2 C contains 16 questions that will test your knowledge on the concepts like remainder Theorem, division algorithm, etc. these questions are quite lengthy to solve and important from your exam point of view.
- Exercise 2 D of RS Aggarwal’s solutions for chapter 2 has 26 questions in total. Questions generally use the concepts of the remainder and factor theorem. These questions are quite tricky, you need to have a better understanding of the remainder theorem and factor theorem for solving it.
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