NCERT Solutions for Class 9 Maths Chapter 2 — Exercise Set 2.1#
The degree of a polynomial in one variable is the highest power of that variable that appears with a non-zero coefficient. A non-zero constant has degree $0$, and the polynomials of degree $1, 2, 3$ are called linear, quadratic, cubic, respectively.
1. Find the degrees of the following polynomials: #
(i) 2x² − 5x + 3
Highest power of $x$ is $2$.
$$\text{Degree} = 2.$$(ii) y³ + 2y − 1
Highest power of $y$ is $3$.
$$\text{Degree} = 3.$$(iii) −9
A non-zero constant.
$$\text{Degree} = 0.$$(iv) 4z − 3
Highest power of $z$ is $1$.
$$\text{Degree} = 1.$$2. Write polynomials of degrees 1, 2 and 3. #
Solution (answers vary)
| Degree | Example polynomial |
|---|---|
| $1$ (linear) | $2x + 5$ |
| $2$ (quadratic) | $x^{2} + 3x - 4$ |
| $3$ (cubic) | $x^{3} - 2x^{2} + x + 1$ |
3. What are the coefficients of x² and x³ in the polynomial x⁴ − 3x³ + 6x² − 2x + 7? #
Solution
Read off the number multiplying each power of $x$:
- Coefficient of $x^{2}$ is $\mathbf{6}$.
- Coefficient of $x^{3}$ is $\mathbf{-3}$.
4. What is the coefficient of z in the polynomial 4z³ + 5z² − 11? #
Solution
There is no $z$ term (i.e. the $z^{1}$ term is missing), so its coefficient is
$$\text{Coefficient of }z = 0.$$5. What is the constant term of the polynomial 9x³ + 5x² − 8x − 10? #
Solution
The constant term is the term without $x$.
$$\text{Constant term} = -10.$$