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RD Sharma Class 8 Solutions Chapter 7 - Factorization (Ex 7.5) Exercise 7.5

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Last updated date: 24th May 2024
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RD Sharma Class 8 Solutions Chapter 7 - Factorization (Ex 7.5) Exercise 7.5 - Free PDF

The RD Sharma Class 8 Solutions Chapter 7 - Factorization will give students a clear understanding of Factorization and how it is used to simplify equations. By using the RD Sharma Class 8 Solutions, students will be able to understand number systems, expressions and equations better. Using these solutions, students will be able to factorize polynomials of degree 2 or 3.

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What is Factorization?

Factorization is the process in which a number is written as a product of its prime factors. It is the process of decomposing a composite (non-prime) number into a product of one or more prime numbers that, when multiplied together, equal the original number.


Factorization Example:


The number 12 can be written as a product of its prime factors as follows: 


12 = 2 x 2 x 3


Therefore, 12 is composed of two 2s and three 3s.


Factorization of Polynomials:

When a polynomial is factored, the individual terms of the polynomial are written as a product of two or more binomials. The degree of the polynomial is the sum of the degrees of the binomials. By using this method, the degree of a polynomial with two terms is always 2. The degree of a polynomial with three terms is 3.


Factorization of Quadratic Equations:

A quadratic equation is an equation in the form ax²+bx+c=0, where a, b and c are real numbers, and x is the unknown. A quadratic equation can be factored into two linear equations. The solutions to the two linear equations will be the roots (or solutions) of the quadratic equation.


Factorization of Cubic Equations:

A cubic equation is an equation in the form ax³+bx²+cx+d=0, where a, b, c and d are real numbers, and x is the unknown. A cubic equation can be factored into two linear equations and a quadratic equation. The solutions to the three linear equations will be the roots (or solutions) of the cubic equation. Knowledge of the quadratic equation will be needed to solve the cubic equation.


The RD Sharma Class 8 Solutions Chapter 7 - Factorization will give students an idea about how Factoring is used to simplify equations. The solutions chapter will also help students understand number systems, expressions and equations. By using this chapter, students will be able to factorize polynomials of degree 2 or 3.

FAQs on RD Sharma Class 8 Solutions Chapter 7 - Factorization (Ex 7.5) Exercise 7.5

1. How will RD Sharma Class 8 Solutions Chapter 7 - Factorization help me score marks?

The solutions of RD Sharma Class 8 Solutions Chapter 7 - Factorization will help you to understand the required concepts. This will enable you to attempt all types of questions that can be asked from this chapter. Attempting more questions will increase your chances of scoring more marks in exams. These solutions will develop a clear understanding of the chapter and its concepts. Students can also ask their doubts and queries related to the chapter on Vedantu's Doubt Discussion Forum. We are always happy to help you. Our team of experts will try their best to reply back the queries as soon as possible. Download the free solution PDF of this chapter and enhance your preparation.

2. What is the degree of a polynomial?

The degree of a polynomial is the sum of the degrees of its monomials. For example, 3x²+2x−3 is a quadratic polynomial because it can be written as the product of two terms, each with degree 1. The degree of this polynomial is 2. Students will get to know about polynomials in RD Sharma Class 8 Chapter 7 - Factorization. These solutions will help them in the Factorization of polynomials of degree 2 or 3. Our dedicated team of mathematics experts has solved all the Ex 7.5 Questions of RD Sharma Chapter 7 - Factorization to make your preparation much easier so that you will be able to score good marks in exams.

3. What does Factorization explain?

It is the process of dividing an expression into monomials. For example, 6x²+5xy can be written as (2x+3y)(2x−3y). Students will get to see practical examples of how factors are used in the Factorization of polynomials in RD Sharma Class 8 Solutions Chapter 7 - Factorization. This chapter is very important from the examination point of view. So, students are advised to practice as many questions as possible to obtain a clear understanding of the concepts. Our expert mathematics teachers have solved all the Ex 7.5 Questions of RD Sharma Chapter 7 - Factorization for your convenience. You can also download the free PDF of this chapter and refer to it later.

4. What is the Factorization of algebraic expression?

Factorization of an algebraic expression is the process of writing a polynomial as the product of its factors. For example, 6x²+5xy can be written as (6x+1)(x+5y). This chapter will help students to understand the concept of Factorization in a better way. The solutions have been explained in detail so that students can attempt all types of questions without any difficulty. The algebraic expressions are written as the product of terms. The students will learn how to factorize the algebraic expressions in RD Sharma Class 8 Solutions Chapter 7 - Factorization.

5. What are the benefits of Factorization?

The benefits of Factorization are as follows:

  1. It helps in the simplification of expressions.

  2. It helps in the solution of equations.

  3. It helps in the determination of roots of equations.

  4. It helps in the approximation of real solutions to equations.

  5. It is a very useful tool for solving problems.

  6. It helps in the preparation of graphs.

  7. It is essential for students appearing for entrance examinations like IIT JEE, AIEEE, etc.

The students will get to know all these benefits of Factorization in RD Sharma Class 8 Solutions Chapter 7 - Factorization. They will also learn how to factorize polynomials of degrees 2 or 3. Our expert mathematics teachers have solved all the Ex 7.5 Questions of RD Sharma Chapter 7 - Factorization for your convenience. Download the free PDF of this chapter and practice as many questions as possible.