## RD Sharma Class 9 Solutions Chapter 6 - Factorization of Polynomials (Ex 6.4) Exercise 6.4 - Free PDF

## FAQs on RD Sharma Class 9 Solutions Chapter 6 - Factorization of Polynomials (Ex 6.4) Exercise 6.4

**1. What is the Remainder theorem?**

The remainder theorem is helpful in finding the remainder on dividing an algebraic expression with another expression, without actually performing the division. The remainder that we obtain when the algebraic expression f(x) is divided by (x - n) is f(n). If f(n) = 0, then (x - n) is a factor of f(x).

**2. What is the Factor theorem?**

The factor theorem efficiently helps in connecting the factors and zeros of the given polynomials. If there is a polynomial of degree n, m is a real number such that (x - m) is a factor of f(x), then if f(m) = 0. Also, f(m) = 0 then (x - m) is a factor of f(x). The factor theorem is very useful for finding the given expression as a factor of a higher degree polynomial expression without doing the division.

**3. What is the Long Division?**

The process called the long division involving polynomials is very similar to the process of the long division of natural numbers. Long division of polynomials is greatly helpful and efficient to find the factors of the given polynomial expression. The division which is resulting in a remainder of zero has the divisor as a factor of the given polynomial expression. Division occurring in the remainder of zero is written as follows:

Dividend = Divisor × Quotient.

Thus, the given polynomial expression gets divided into two main factors.

**4. How to obtain Greatest common factors?**

The process of obtaining the greatest common factor for two or more terms of the given polynomial includes two simple steps. Firstly, we split each of the terms into its prime factors. Then, take as many common factors that are possible from the given terms.

**5. How to factorise polynomials in 3 degrees?**

The process of factorization of polynomials in 3 degrees involves three very simple steps. Firstly, for the given n degree polynomial f(x), substitute a value 'm' such that f(m) = 0, and (x - m) is a factor. In the second part, divide f(x) by (x - m) to obtain a quadratic equation. Finally, we do factorization of the quadratic equation to obtain its two factors. Hence, we can obtain all three factors of the 3-degree polynomial. Visit the official website of Vedantu or log on to the app for a detailed explanation of all of the above.