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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
Solution:
(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?
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