NCERT Solutions for Class 9 Maths Exercise 2.1 Question 3
Understanding the Question 🧐
This question asks us to create two specific types of polynomials. Before we create them, let’s understand the terms:
- A Binomial is a polynomial that has exactly two terms (e.g., &&x + 5&&).
- A Monomial is a polynomial that has exactly one term (e.g., &&7x^3&&).
- The Degree of a polynomial is the highest power (exponent) of the variable in it.
So, we need to provide one example for each of the two cases described in the question.
Give one example each of a binomial of degree 35, and of a monomial of degree 100.
Part (i): Example of a Binomial of Degree 35 📝
Requirements:
- The polynomial must have exactly two terms.
- The highest power of the variable in the polynomial must be 35.
Construction:
To satisfy the degree requirement, one of the terms must be of the form &&ax^{35}&&. To make it a binomial, we just need to add or subtract any other term with a lower power. The second term can have any whole number power less than 35.
Example:
A simple example is &&x^{35} + 10&&.
Other Possible Answers:
There are infinitely many correct answers. Some other examples are:
- &&3y^{35} – y^2&&
- &&z^{35} + 5z^{34}&&
- &&-2t^{35} + 7&&
Part (ii): Example of a Monomial of Degree 100 📝
Requirements:
- The polynomial must have exactly one term.
- The power of the variable in the term must be 100.
Construction:
We need a single term where the variable is raised to the power of 100. We can use any variable and any non-zero coefficient.
Example:
A simple example is &&7t^{100}&&.
Other Possible Answers:
Again, there are infinitely many correct answers. Some other examples are:
- &&x^{100}&&
- &&-15y^{100}&&
- &&\sqrt{3}z^{100}&&
- Monomial = 1 term.
- Binomial = 2 terms.
- Trinomial = 3 terms.
- The Degree is determined by the highest exponent of the variable.
FAQ ❓
Q: What is the difference between a monomial and a binomial?
A: A monomial is a polynomial with exactly one term (e.g., &&5x^2&&). A binomial is a polynomial with exactly two terms (e.g., &&5x^2 + 3x&&).
Q: What is the degree of a polynomial?
A: The degree of a polynomial is the highest exponent (power) of the variable in any of its terms. For example, in the polynomial &&7x^5 + 2x^3 – 10&&, the highest power is 5, so the degree is 5.
Q: Is &&x^{35} + 4&& a valid example of a binomial of degree 35?
A: Yes, it is a perfect example. It has two terms (making it a binomial) and the highest power of the variable &&x&& is 35 (making its degree 35).
Further Reading 📖
To learn more about the types of polynomials and their degrees, you can refer to the official NCERT textbook for Class 9 Maths, Chapter 2. More resources are available on the NCERT website at https://ncert.nic.in/.
