NCERT Solutions for Class 9 Maths Exercise 2.1 Question 5
Understanding the Question 🧐
This question asks us to classify polynomials based on their degree. The degree is the highest power of the variable in the polynomial. The classifications are:
- Linear Polynomial: A polynomial of degree 1.
- Quadratic Polynomial: A polynomial of degree 2.
- Cubic Polynomial: A polynomial of degree 3.
Our task is to find the degree of each given polynomial and then name it accordingly.
Classify the following as linear, quadratic and cubic polynomials:
(i) &&x^2 + x&& (ii) &&x – x^3&& (iii) &&y + y^2 + 4&& (iv) &&1 + x&& (v) &&3t&& (vi) &&r^2&& (vii) &&7x^3&&
Solutions and Classifications 📝
(i) &&x^2 + x&&
Therefore, it is a Quadratic polynomial.
(ii) &&x – x^3&&
Therefore, it is a Cubic polynomial.
(iii) &&y + y^2 + 4&&
Therefore, it is a Quadratic polynomial.
(iv) &&1 + x&&
Therefore, it is a Linear polynomial.
(v) &&3t&&
Therefore, it is a Linear polynomial.
(vi) &&r^2&&
Therefore, it is a Quadratic polynomial.
(vii) &&7x^3&&
Therefore, it is a Cubic polynomial.
Conclusion and Summary ✅
Here is a summary of the classification for each polynomial:
| Polynomial | Highest Power (Degree) | Classification |
|---|---|---|
| &&x^2 + x&& | 2 | Quadratic |
| &&x – x^3&& | 3 | Cubic |
| &&y + y^2 + 4&& | 2 | Quadratic |
| &&1 + x&& | 1 | Linear |
| &&3t&& | 1 | Linear |
| &&r^2&& | 2 | Quadratic |
| &&7x^3&& | 3 | Cubic |
- Degree 1 ➡️ Linear (like a straight line graph)
- Degree 2 ➡️ Quadratic (like a parabola graph)
- Degree 3 ➡️ Cubic
FAQ ❓
Q: How are polynomials classified as linear, quadratic, or cubic?
A: Polynomials are classified based on their degree, which is the highest power of the variable. A polynomial of degree 1 is called linear. A polynomial of degree 2 is called quadratic. A polynomial of degree 3 is called cubic.
Q: Is &&3t&& a linear polynomial?
A: Yes, &&3t&& is a linear polynomial. The variable ‘&&t&&’ can be written as &&t^1&&, so its power is 1. Since the highest power (degree) is 1, the polynomial is linear.
Q: What’s the difference between a quadratic polynomial and a cubic polynomial?
A: The difference is their degree. A quadratic polynomial has a degree of 2 (the highest power of the variable is 2, like in &&x^2 + 5&&), while a cubic polynomial has a degree of 3 (the highest power of the variable is 3, like in &&x^3 – 2x&&).
Further Reading 📖
To learn more about classifying polynomials, 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/.
