# NCERT Solutions For Class 9 Maths Chapter 2 Polynomials Ex 2.1

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Textbook | NCERT |

Board | CBSE |

Category | NCERT Solutions |

Class | Class 9 |

Subject | Maths |

Chapter | Chapter 2 |

Exercise | Class 9 Chapter 2 Polynomials Exercise 2.1 |

Number of Questions Solved | 5 |

## NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.1

**NCERT TEXTBOOK EXERCISES**

**Question 1. Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.**

**(i) 4x ^{2} – 3x + 7**

**(ii) y**

^{2}+ √2**(iii) 3 √t + t√2**

**(iv) y+ 2/y**

**(v) x**

^{10}+ y^{3}+t^{50}**Solution:**

**(i)** 4x^{2} – 3x + 7 is an expression having only non-negative integral powers of x. So, it is a polynomial.**(ii)** y^{2} +√2 is an expression having only non-negative integral power of y. So, it is a polynomial.**(iii)** 3√t + √2 is an expression in which one term namely 3√t has rational power of f. So, it is not a polynomial.**(iv)** y+ 2/y is an expression in which one term namely 2/y ⇒ i.e., 2y^{-1} has negative power of y. So, it is not a polynomial.**(v)** x^{10} + y^{3} + t^{50} is an expression which has 3 variables.

**Question 2. Write the coefficients of x ^{2} in each of the following**

**(i) 2 + x ^{2} + x(ii) 2 – x2 + x3**

**(iii) π/2 x**

(iv) √2 x – 1

^{2}+ x(iv) √2 x – 1

**Solution:**

**(i)** The coefficient of x^{2} in 2 + x^{2} + x is 1.**(ii)** The coefficient of x^{2} in 2 – x^{2} + x^{3} is – 1.**(iii)** The coefficient of x^{2} in π/2 x^{2}+ x is π/2 .**(iv)** The coefficient of x^{2} in **√**2 x -1 is 0

**Question 3. Give one example each of a binomial of degree 35, and of a monomial of degree 100.**

**Solution:**

**(i)** y^{35} + 2 is a binomial of degree 35.**(ii)** y^{100} is a monomial of degree 100.

**Question 4. Write the degree of each of the following polynomials.**

**(i) 5x ^{3}+4x^{2} + 7x**

**(ii) 4 – y**

^{2}(iii) 5f – √7**(iv) 3**

**Solution:**

(i) In a polynomial 5x^{3} + 4x^{2} + 7x, the highest power of variable x is 3, hence degree of polynomial is 3.

(ii) In a polynomial 4 – y^{2}, the highest power of variable y = 2, hence degree of polynomial is 2.

(iii) In a polynomial 5t – √7 , the highest power of variable t = 1, hence the degree of polynomial is 1.

(iv) In a polynomial 3, the highest power of variable y = 0, hence the degree of polynomial is 0.

**Question 5. 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}

**Solution:**

(i) The degree of polynomial x^{2} + 2 is 2, hence it is a quadratic polynomial.

(ii) The degree of polynomial x – x^{3} is 3, hence it is a cubic polynomial.

(iii) The degree of polynomial y + y^{2} + 4 is 2, hence it is a quadratic polynomial.

(iv) The degree of polynomial 1 + x is 1, hence it is a linear polynomial.

(v) The degree of polynomial 3t is 1, hence it a linear polynomial.

(vi) The degree of polynomial r^{2} is 2, hence it is a quadratic polynomial.

(vii) The degree of polynomial 7x^{3} is 3, hence it is a cubic polynomial.

## NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Exercise 2.1 PDF

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