RBSE Solutions for Class 9 Maths Chapter 3 Polynomial Ex 3.1 is part of RBSE Solutions for Class 9 Maths. Here we have given Rajasthan Board RBSE Class 9 Maths Solutions Chapter 3 Polynomial Exercise 3.1.

Board |
RBSE |

Class |
Class 9 |

Subject |
Maths |

Chapter |
Chapter 3 |

Chapter Name |
Polynomial |

Exercise |
Ex 3.1 |

Number of Questions Solved |
7 |

Category |
RBSE Solutions |

## Rajasthan Board RBSE Class 9 Maths Solutions Chapter 3 Polynomial Ex 3.1

Question 1.

Which of the following expressions are polynomials in (RBSESolutions.com) one variable and which are not? State reasons for your answers.

(i) 3x² – 5x + 13

(ii) y² + 2√3

(iii) y + \(\frac { 3 }{ y }\)

(iv) 3

(v) 2√x + √3x

(vi) x^{12} + y^{3} + t^{20}

Solution.

(i) 3x² – 5x + 13 is a polynomial in one variable, because (RBSESolutions.com) degree of the variable x is a whole number.

(ii) y² + 2√3 is a polynomial in variable because degree of the variable y is a whole number i.e. 2.

(iii) y + \(\frac { 3 }{ y }\) is not a polynomial because degree of the variable y in second term is – 1.

(iv) 3 is a constant polynomial.

(v) 2√x + √3x is not a polynomial because degree of x in first term is \(\frac { 1 }{ 2 }\)

(vi) x^{12} + y^{3} + t^{20} contain more than one variables. Hence it is not a polynomial in one variable.

Question 2.

Write the coefficient of x² in each (RBSESolutions.com) of the following:

(i) 12 + 3x + 5x^{2}

(ii) 7 – 11x + x^{3}

(iii) √3x – 7

(iv) \(\frac { \pi }{ 2 } { x }^{ 2 }+x\)

Solution.

(i) In the given polynomial

p(x) = 12 + 3x + 5x^{2}, the coefficient of x^{2} is 5.

(ii) In the (RBSESolutions.com) given polynomial

p(x) = 7 – 11x + x^{3}, the coefficient of x^{2} is 0.

(iii) In the given polynomial

p(x) = √3x – 7, the coefficient of x^{2} is 0.

(iv) In the given polynomial

p(x) = \(\frac { \pi }{ 2 } { x }^{ 2 }+x\), the coefficient of x^{2} is \(\frac { \pi }{ 2 } \).

Question 3.

Given an example of (RBSESolutions.com) a binomial of degree 45.

Solution.

A binomial of degree 45 is ax^{45} + b, where a non-zero real number and is called coefficient of x^{45} and b ≠ 0.

Question 4.

Give an example of a monomial of degree 120.

Solution.

A monomial of degree 120 is ax^{120}, where a is non-zero real number, which is also coefficient of x^{120}

Question 5.

Give an example of (RBSESolutions.com) a trinomial of degree 8.

Solution.

2x^{8} + 3x^{4} + 5x.

Question 6.

Can you write another terms in the example given question no. 3, 4, 5. If yes give two examples of each.

Solution.

(i) 2x^{45} + 3, \(\frac { 11 }{ 2 }\)x^{45} + 7

(ii) x^{120}, 7x^{120}

(iii) 7x^{8} + 7x^{5} + 1, 17x^{8} + 2x^{5} + x.

The above example can very from person to person.

Question 7.

Write the degree of (RBSESolutions.com) each of the following polynomials.

(i) 12 – 3x + 2x^{2}

(ii) 5y – √2

(iii) 9

(iv) 3 + 4t^{2}

Solution.

(i) In 12 – 3x + 2x^{2}, the highest power of the variable x is 3, so its degree is 3.

(ii) In 5y – √2 , the highest power of the variable y is 1, so its degree 1.

(iii) 9 is a constant polynomial, and degree of (RBSESolutions.com) a constant polynomial is always (0) zero.

(iv) In 3 + 4t^{2}, the highest power of the variable t is 2, so its degree is 2.

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