RD Sharma Solutions for Class 9 Maths Chapter 6 Factorization of Polynomials
The RD Sharma Solutions for Class 9 Maths Chapter 6 - Factorization of Polynomials are available to help students understand the topic better. In this chapter, students will explore important concepts such as polynomials, the degree of a polynomial, factors, multiples, and zeros. A polynomial is an expression made up of variables, constants, and exponents, and these are combined using operations like addition, subtraction, multiplication, and division (but not division by a variable). Depending on how many terms the expression has, polynomials can be monomials, binomials, or trinomials.
Students can easily download the RD Sharma Solutions for Class 9 from the links below. These solutions, created by IL subject-matter experts, are designed to make the concepts easier to understand. By practicing these solutions, students can work towards achieving high scores in their exams. The RD Sharma Solutions are a great resource for mastering the material.
RD Sharma Solution for Class 9 Chapter 6 - Download PDF
Here are the RD Sharma Class 9 Maths Chapter 6 Solutions, designed to help students prepare effectively for their exams. By referring to these solutions and practicing the problems, students can boost their confidence and improve their scores.
RD Sharma Solution for Class 9 Chapter 6 - Question with Answer
RD Sharma Solutions for Class 9 Maths Chapter 6 - Factorization of Polynomials, divided into exercises:
Here are 30-40 questions with answers based on RD Sharma Solutions for Class 9 Chapter 6 - Factorization of Polynomials:
1. What is a polynomial?
Answer: A polynomial is an algebraic expression consisting of variables, constants, and exponents combined using addition, subtraction, and multiplication operations (excluding division by a variable).
2. What are the types of polynomials based on the number of terms?
Answer: Polynomials are classified into:
- Monomial (one term)
- Binomial (two terms)
- Trinomial (three terms)
3. What is the degree of a polynomial?
Answer: The degree of a polynomial is the highest power of the variable present in the polynomial expression.
4. What are the factors of a polynomial?
Answer: Factors of a polynomial are expressions that can be multiplied together to get the original polynomial.
5. What are zeros of a polynomial?
Answer: The zeros of a polynomial are the values of the variable that make the polynomial equal to zero.
6. Factorize: x² + 7x + 12
Answer: (x + 3)(x + 4)
7. Factorize: x² – 5x + 6
Answer: (x – 2)(x – 3)
8. Factorize: x² + 10x + 21
Answer: (x + 3)(x + 7)
9. Factorize: 2x² + 5x – 3
Answer: (2x – 1)(x + 3)
10. What is the difference between a monomial, binomial, and trinomial?
Answer: A monomial has one term, a binomial has two terms, and a trinomial has three terms.
11. How do you factorize a quadratic polynomial?
Answer: A quadratic polynomial is factorized by finding two numbers that multiply to give the constant term and add up to give the coefficient of the linear term.
12. Factorize: 4x² – 12x
Answer: 4x(x – 3)
13. Factorize: 9x² + 6x – 12
Answer: 3(3x² + 2x – 4)
14. What is the general form of a quadratic polynomial?
Answer: The general form of a quadratic polynomial is ax² + bx + c, where a, b, and c are constants, and a ≠ 0.
15. Factorize: x² – 9
Answer: (x – 3)(x + 3)
16. Factorize: 5x² + 20x
Answer: 5x(x + 4)
17. What does it mean for a polynomial to be factorized completely?
Answer: A polynomial is said to be factorized completely when it is expressed as the product of irreducible polynomials, i.e., polynomials that cannot be factored further.
18. What are the steps to factorize a polynomial using grouping?
Answer:
- Split the middle term into two terms.
- Group the terms in pairs.
- Factor out the common factor from each group.
- Factor out the common binomial.
19. Factorize: 3x² + 7x + 4
Answer: (3x + 4)(x + 1)
20. What is the method of factoring by grouping?
Answer: Factoring by grouping involves grouping terms of the polynomial in pairs, factoring out the common factor from each group, and then factoring out the common binomial factor.
21. Factorize: x² + 4x – 5
Answer: (x + 5)(x – 1)
22. Factorize: x² – 4x – 5
Answer: (x – 5)(x + 1)
23. What is a binomial?
Answer: A binomial is a polynomial with exactly two terms, for example, x + 3 or 2x – 5.
24. What is the product of two binomials called?
Answer: The product of two binomials is called a quadratic polynomial.
25. Factorize: x² + 5x + 6
Answer: (x + 2)(x + 3)
26. How do you factorize a cubic polynomial?
Answer: A cubic polynomial is typically factorized by looking for common factors or using methods such as synthetic division or grouping.
27. Factorize: x³ – x² – 6x
Answer: x(x² – x – 6) = x(x – 3)(x + 2)
28. Factorize: 4x² – 25
Answer: (2x – 5)(2x + 5)
29. Factorize: 6x² + 11x – 35
Answer: (3x – 5)(2x + 7)
30. What is the significance of factorization in mathematics?
Answer: Factorization helps in simplifying expressions, solving equations, and finding the roots of polynomials. It is also useful in solving real-life problems related to areas, volumes, and other quantities.
31. Factorize: x² + 2x – 35
Answer: (x + 7)(x – 5)
32. What is meant by the factor theorem?
Answer: The factor theorem states that if a polynomial f(x) has a factor (x – a), then f(a) = 0.
33. Factorize: x³ – 3x² – 4x
Answer: x(x² – 3x – 4) = x(x – 4)(x + 1)
34. How do you check if a factorization is correct?
Answer: Multiply the factors and check if you get back the original polynomial. If yes, the factorization is correct.
35. Factorize: 2x² – 7x – 3
Answer: (2x + 1)(x – 3)
36. What is a trinomial?
Answer: A trinomial is a polynomial with exactly three terms, for example, x² + 5x + 6.
37. Factorize: x² + 6x + 9
Answer: (x + 3)(x + 3) or (x + 3)²
38. Factorize: 3x² + 5x – 2
Answer: (3x – 1)(x + 2)
39. What is the method to factorize a polynomial completely?
Answer: To factorize a polynomial completely, first factor out any common factors, then use methods like grouping, splitting the middle term, or applying special identities (difference of squares, perfect square trinomials, etc.).
40. Factorize: 4x² + 13x + 9
Answer: (4x + 3)(x + 3)
FAQs on RD Sharma Solutions for Class 9 Maths Chapter 6
Are RD Sharma Solutions for Class 9 Maths Chapter 6 suitable for CBSE students?
Yes, RD Sharma Solutions for Class 9 Maths Chapter 6 are absolutely suitable for CBSE students. These solutions are designed according to the CBSE curriculum and help students understand the concept of factorization of polynomials in a detailed and easy-to-understand manner.
Can I use Class 9 RD Sharma Factorization of Polynomials Solutions for exam preparation?
Absolutely! RD Sharma Factorization of Polynomials Solutions are great for exam preparation. By practicing the problems and referring to the solutions, students can gain a strong conceptual understanding and be well-prepared for exams. These solutions also cover a wide range of problems that help build confidence and improve problem-solving skills.
Is it good to use the RD Sharma Class 9 Solutions Factorization of Polynomials?
Yes, using RD Sharma Class 9 Solutions for Factorization of Polynomials is highly recommended. These solutions provide step-by-step explanations and help students grasp the concepts of polynomials and factorization with ease. The explanations are simple, and the variety of practice problems ensures a thorough understanding of the topic.
What is the meaning of Polynomials, according to RD Sharma Solutions for Class 9 Maths Chapter 6?
According to RD Sharma Solutions for Class 9 Maths Chapter 6, a polynomial is an algebraic expression made up of variables, constants, and exponents combined using mathematical operations such as addition, subtraction, and multiplication. It does not involve division by a variable. Examples include expressions like 2x² + 3x + 4, where x is the variable.
Where can I download RD Sharma Solutions for Class 9 Maths Chapter 6?
You can easily download RD Sharma Solutions for Class 9 Maths Chapter 6 from various educational websites like BYJU'S, Vedantu, and others that offer free PDF downloads. Alternatively, you can search for specific links that offer chapter-wise solutions for the RD Sharma textbook.
Are RD Sharma Solutions for Class 9 Maths Chapter 6 suitable for CBSE students?
Yes, RD Sharma Solutions for Class 9 Maths Chapter 6 are absolutely suitable for CBSE students. These solutions are designed according to the CBSE curriculum and help students understand the concept of factorization of polynomials in a detailed and easy-to-understand manner.