RBSE Solutions for Class 9 Maths Chapter 3 Polynomial Ex 3.1

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.

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) x¹² + y³ + t²⁰
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) x¹² + y³ + t²⁰ 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 + 5x²
(ii) 7 – 11x + x³
(iii) √3x – 7
(iv) \(\frac { \pi }{ 2 } { x }^{ 2 }+x\)
Solution.
(i) In the given polynomial
p(x) = 12 + 3x + 5x², the coefficient of x² is 5.
(ii) In the (RBSESolutions.com) given polynomial
p(x) = 7 – 11x + x³, the coefficient of x² is 0.
(iii) In the given polynomial
p(x) = √3x – 7, the coefficient of x² is 0.
(iv) In the given polynomial
p(x) = \(\frac { \pi }{ 2 } { x }^{ 2 }+x\), the coefficient of x² is \(\frac { \pi }{ 2 } \).

Question 3.
Given an example of (RBSESolutions.com) a binomial of degree 45.
Solution.
A binomial of degree 45 is ax⁴⁵ + b, where a non-zero real number and is called coefficient of x⁴⁵ and b ≠ 0.

Question 4.
Give an example of a monomial of degree 120.
Solution.
A monomial of degree 120 is ax¹²⁰, where a is non-zero real number, which is also coefficient of x¹²⁰

Question 5.
Give an example of (RBSESolutions.com) a trinomial of degree 8.
Solution.
2x⁸ + 3x⁴ + 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) 2x⁴⁵ + 3, \(\frac { 11 }{ 2 }\)x⁴⁵ + 7
(ii) x¹²⁰, 7x¹²⁰
(iii) 7x⁸ + 7x⁵ + 1, 17x⁸ + 2x⁵ + 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 + 2x²
(ii) 5y – √2
(iii) 9
(iv) 3 + 4t²
Solution.
(i) In 12 – 3x + 2x², 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 + 4t², the highest power of the variable t is 2, so its degree is 2.

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