Master Class 9 Maths Polynomials with Rbse Solutions for Exercise 2.1. Find the degree, coefficient, and classify linear, quadratic, and cubic polynomials. Step-by-step answers for CBSE/RBSE students.


1. Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.
A polynomial is an expression where the powers (exponents) of the variable(s) are non-negative integers ($\{0, 1, 2, 3, \dots\}$).
| Expression | Polynomial in One Variable? | Reason |
| (i) $4x^2 – 3x + 7$ | Yes | The only variable is $x$, and its powers (2, 1, and 0 for the constant 7) are non-negative integers. |
| (ii) $y^2 + \sqrt{2}$ | Yes | The only variable is $y$, and its power (2) is a non-negative integer. |
| (iii) $3\sqrt{t} + t\sqrt{2}$ | No | The power of the variable $t$ in the first term is $\frac{1}{2}$ ($3t^{\frac{1}{2}}$), which is not an integer. |
| (iv) $y + \frac{2}{y}$ | No | The second term is $2y^{-1}$. The power of $y$ is $-1$, which is a negative integer. |
| (v) $x^{10} + y^3 + t^{50}$ | No | This is a polynomial, but it has three variables ($x, y, t$), not one. |
2. Write the coefficients of $x^2$ in each of the following:
The coefficient of a term is the number multiplied by that term.
| Expression | Term with x2 | Coefficient of x2 |
| (i) $2 + x^2 + x$ | $1 \cdot x^2$ | 1 |
| (ii) $2 – x^2 + x^3$ | $-1 \cdot x^2$ | -1 |
| (iii) $\frac{\pi}{2} x^2 + x$ | $\frac{\pi}{2} x^2$ | $\frac{\pi}{2}$ |
| (iv) $\sqrt{2}x – 1$ | (Missing term) | 0 (We can write this as $0 \cdot x^2 + \sqrt{2}x – 1$) |
3. Give one example each of a binomial of degree 35, and of a monomial of degree 100.
- Binomial of degree 35: A binomial has two non-zero terms, and the degree is the highest power of the variable.
- Example: $\mathbf{x^{35} + 5}$ (or $y^{35} – 10$, etc.)
- Monomial of degree 100: A monomial has one non-zero term, and the degree is the power of the variable.
- Example: $\mathbf{7x^{100}}$ (or $\sqrt{2}y^{100}$, etc.)
4. Write the degree of each of the following polynomials:
The degree of a polynomial is the highest power of the variable in the expression.
| Polynomial | Highest Power | Degree |
| (i) $5x^3 + 4x^2 + 7x$ | $x^3$ | 3 |
| (ii) $4 – y^2$ | $y^2$ | 2 |
| (iii) $5t – \sqrt{7}$ | $t^1$ | 1 |
| (iv) $3$ | (Constant term, $3x^0$) | 0 |
5. Classify the following as linear, quadratic and cubic polynomials:
Polynomials are classified based on their degree:
- Linear: Degree 1
- Quadratic: Degree 2
- Cubic: Degree 3
| Polynomial | Degree | Classification |
| (i) $x^2 + x$ | 2 | Quadratic |
| (ii) $x – x^3$ | 3 | Cubic |
| (iii) $y + y^2 + 4$ | 2 | Quadratic |
| (iv) $1 + x$ | 1 | Linear |
| (v) $3t$ | 1 | Linear |
| (vi) $r^2$ | 2 | Quadratic |
| (vii) $7x^3$ | 3 | Cubic |
