NCERT Solutions for Class 9 Maths Chapter 2 Polynomials

Ans : (i) \(4 x^{2}-3 x+7   \)
Yes, this expression is a polynomial in one variable x.
(ii) \(y^{2}+\sqrt{2}  \)
Yes, this expression is a polynomial in one variable x.
(iii) \( 3 \sqrt{t}+t \sqrt{2}  \)
No It can be observed that the exponent of variable t in term \( 3 \sqrt{t} {\text { is }} \frac{1}{2}  \)  which is not a whole number .Therefore this expression is not a polynomial.
(iv) \(y+\frac{2}{y}   \) No It can be observed that the exponent of variable t in term \( \frac{2}{y} {\text { is }-1,}  \)  which is not a whole number .Therefore this expression is not a polynomial.
(v) \(  x^{2}+y^{3}+t \) No It can be observed that this expression is a polynomial in 3 variables x,y and and t .Therefore , this expression is not a polynomial . 

Ans : (i) \( 2+x^{2}+x  \)  
In the above expression the coefficient of \(  x^{2} \) is \( 1.  \)  
(ii) \( 2-x^{2}+x^{3}  \)  
In the above expression the coefficient of \( x^{2}  \) is \(  -1 \)  
(iii) \(  \frac{\pi}{2} x^{2}+x \)  
In the above expression the coefficient of \(  x^{2} \) is \( \frac{\pi}{2}  \)  
(iv) \(\sqrt{2} x-1   \)  \(  0 x^{2}+\sqrt{2} x-1 \) or \( 0 x^{2}+\sqrt{2} x-1  \)   
In the above expression the coefficient of \(x^{2}   \) is \( 0  \) 

Ans : Degree of a polynomial is the highest power of the variable in the polynomial. Binomial has two terms in it. Therefore, binomial of degree 35 can be written as \(  x^{35}+x^{34} \) Monomial has only one term in it. Therefore, monomial of degree 100 can be written as \( X^{100}  \) 

Ans : Degree of a polynomial is the highest power of the variable in the polynomial.
(i) \( 5 x^{3}+4 x^{2}+7 x \)
This is a polynomial in a variable x and the highest power of variable x is 3 . Therefore, the degree of this polynomial is 3.
(ii) \( 4-y^{2}  \) This is a polynomial in variable y and the highest power of variable y is 2. Therefore, the degree of this polynomial is 2 .
(iii) \(  5 t-\sqrt{7} \) This is a polynomial in variable t and the highest power of variable t is 1. Therefore, the degree of this polynomial is 1.
(iv) 3 This is a constant polynomial. Degree of a constant polynomial is always 0. 

Ans : Linear polynomial, quadratic polynomial, and cubic polynomial has its degrees as 1, 2, and 3 respectively.
(i) \(x^{2}+x  \) is a quadratic polynomial as its degree is 2 .
(ii) \(x-x^{3} \) is a cubic polynomial as its degree is 3 .
(iii) \(y+y^{2}+4 \) is a quadratic polynomial as its degree is 1.
(iv) \( 1+x  \) is a linear polynomial as its degree is 1.
(v) \( 3 t  \) is a linear polynomial as its degree is 1.
(vi) \(  r^{2} \) is a quadratic polynomial as its degree is 2.
(vii) \(7 x^{3}   \)  s a cubic polynomial as its degree is 3 .