Rbse Solutions for Class 9 Maths Chapter 2 Exercise 2.1 | Polynomials, Degree, Coefficient

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.

Rbse Solutions for Class 9 Maths Chapter 2 Exercise 2.1 | Polynomials, Degree, Coefficient
Rbse Solutions for Class 9 Maths Chapter 2 Exercise 2.1 | Polynomials, Degree, Coefficient

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 ($\{0, 1, 2, 3, \dots\}$).

ExpressionPolynomial in One Variable?Reason
(i) $4x^2 – 3x + 7$YesThe only variable is $x$, and its powers (2, 1, and 0 for the constant 7) are non-negative integers.
(ii) $y^2 + \sqrt{2}$YesThe only variable is $y$, and its power (2) is a non-negative integer.
(iii) $3\sqrt{t} + t\sqrt{2}$NoThe power of the variable $t$ in the first term is $\frac{1}{2}$ ($3t^{\frac{1}{2}}$), which is not an integer.
(iv) $y + \frac{2}{y}$NoThe second term is $2y^{-1}$. The power of $y$ is $-1$, which is a negative integer.
(v) $x^{10} + y^3 + t^{50}$NoThis 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.

ExpressionTerm with x2Coefficient 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.

PolynomialHighest PowerDegree
(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
PolynomialDegreeClassification
(i) $x^2 + x$2Quadratic
(ii) $x – x^3$3Cubic
(iii) $y + y^2 + 4$2Quadratic
(iv) $1 + x$1Linear
(v) $3t$1Linear
(vi) $r^2$2Quadratic
(vii) $7x^3$3Cubic
Scroll to Top