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Factorization of Polynomials - Chapter 6, Class 9 (Mathematics)
Factorization of polynomials is the 6th Chapter of Mathematics in Class 9. Factoring a polynomial can be defined as the expression of the polynomial as a product of two or more than two factors and so on. In mathematics, a polynomial is an expression containing indeterminate and coefficients which involves the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. An illustration of a polynomial of a single indeterminate x is x² − 4x + 7.
In this chapter, students shall cover the algebraic expressions which are called polynomial expressions, and also learn the terms related to them. They will also study the Remainder Theorem and Factor Theorem and their use in the factorisation of polynomials.
FAQs on RD Sharma Class 9 Solutions Chapter 6 - Factorization of Polynomials (Ex 6.5) Exercise 6.5
1. What are the degrees of a polynomial and how to find it?
The degree of a polynomial is the largest power of the variable in a polynomial expression. The degree indicates the largest exponential power in the polynomial (not including the coefficients).
An example of finding degrees of a polynomial-
What is the degree of each of the polynomials given below?
(i) x⁵ – x⁴ + 3
(ii) 2 – y² – y³+ 2y⁹
(i) The largest power of the variable is 5. Therefore, the degree of the polynomial is 5.
(ii) The largest power of the variable is 9. So, the degree of the polynomial is 9.
2. What is a homogenous degree?
A polynomial of degree 0 is always homogeneous. To find whether the given polynomial expression is homogeneous or not, the degree of the terms in the polynomial is important. We can consider this example, 3x³ + 2xy³+4y³ is a multivariable polynomial. To check whether the polynomial expression is homogeneous, you have to determine the degree of each term. If all the degrees of the term are equal, then the polynomial expression is also said to be homogeneous. In the given equation, the degree of all the terms is 3. Hence, in the discussed example is a homogeneous polynomial of degree 3.
3. Why is it called polynomial equations?
The word poly means numerous and nominal means term in the polynomial. The word polynomial joins two different roots: the Greek poly, meaning numerous, and the Latin nomen, or name. It came from the term binomial by replacing the Latin root bi- with the Greek poly- which can be defined as the sum of many terms or monomials. Therefore, polynomials are algebraic expressions that are composed of two or more two algebraic terms. The algebraic terms are constant, exponents and variables.
4. Is this chapter helpful for IIT JEE?
Yes, the chapter can be helpful for your IIT JEE examinations as well as other entrance examinations. For this, you can take the help of Vedantu subject-experts who can guide you with your preparations and also help you under the weightage of marks that the chapter factorization of polynomial expressions carries. Likewise, you can get your doubts cleared by the experts and download the PDF version of all the free study materials provided by Vedantu.
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