NCERT Solutions Class 9 Mathematics
Exercise 2.1
Q.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} + $\sqrt{2}$ (iii) 3$\sqrt{\mathrm{t}}$ + t$\sqrt{2}$
(iv) y + $\frac{2}{\mathrm{y}}$ (v) x^{10} + y^{3} + t^{50}
Q.2: Write the coefficients of x^{2} in each of the following:
 2 + x^{2} + x
 2  x^{2} + x^{3}
 $\frac{\mathrm{\pi}}{2}$ x^{2} + x
 $\sqrt{2}$x  1
Q.3. Give one example each of a binomial of degree 35, and of a monomial of degree 100.
Q.4: Write the degree of each of the following polynomials:
 5x^{3} + 4x^{2} + 7x
 4  y^{2}
 5t  $\sqrt{7}$
 3
Q.5: Classify the following as linear, quadratic and cubic polynomial:
 x^{2} + x

 x  x^{3}

 y + y^{2} +4

 1 + x

 t

 r^{2 }

 7x^{3}
 
NCERT Solutions Class 9 Mathematics
Exercise 2.1
Q.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} + $\sqrt{2}$ (iii) 3$\sqrt{\mathrm{t}}$ + t$\sqrt{2}$
(iv) y + $\frac{2}{\mathrm{y}}$ (v) x^{10} + y^{3} + t^{50}
Solution:
 4x^{2}  3x + 7: This is an expression with only one variable x with +ve integer powers. Hence, this is a polynomial in one variable.
 y^{2} + $\sqrt{2}$: This is an expression with only one variable y with +ve integer powers. Hence, this is a polynomial in one variable.
 3$\sqrt{\mathrm{t}}$ + t$\sqrt{2}$: This is an expression with only one variable t but one of the powers of t is $\frac{1}{2}$ (in 3$\sqrt{\mathrm{t}}$), which is not +ve integer. Hence, this is not a polynomial.
 y + $\frac{2}{\mathrm{y}}$ = y + 2y^{1}: This is an expression with only one variable y but one of the powers of y is 1, which is not +ve integer. Hence, this is not a polynomial.
 x^{10} + y^{3} + t^{50}:There are three variable x, y and t, hence, this is not a polynomial in one variable.
Q.2: Write the coefficients of x^{2} in each of the following:
 2 + x^{2} + x
 2  x^{2} + x^{3}
 $\frac{\mathrm{\pi}}{2}$ x^{2} + x
 $\sqrt{2}$x  1
Solution:
 2 + x^{2} + x: coefficients of x^{2} = 1
 2  x^{2} + x^{3}: coefficients of x^{2} = 1
 $\frac{\mathrm{\pi}}{2}$ x^{2} + x: coefficients of x^{2} = $\frac{\mathrm{\pi}}{2}$
 $\sqrt{2}$x  1: coefficients of x^{2} = 0
Q.3. Give one example each of a binomial of degree 35, and of a monomial of degree 100.
Solution:
Binomial of degree 35: 4x^{35}+7
Monomial of degree 100: 3x^{100}
Q.4: Write the degree of each of the following polynomials:
 5x^{3} + 4x^{2} + 7x
 4  y^{2}
 5t  $\sqrt{7}$
 3
Solution:
 5x^{3} + 4x^{2} + 7x : degree 3
 4  y^{2 }: degree 2
 5t  $\sqrt{7}$ : degree 1
 3 : degree 0.
Q.5: Classify the following as linear, quadratic and cubic polynomial:
 x^{2} + x

 x  x^{3}

 y + y^{2} +4

 1 + x

 t

 r^{2 }

 7x^{3}
 
Solution:
 x^{2} + x: Quadratic Polynomial

 x  x^{3}: Cubic Polynomial

 y + y^{2} +4: Quadratic Polynomial

 1 + x: Linear Polynomial

 3t: Linear Polynomial

 r^{2}: Quadratic Polynomial

 7x^{3}: Cubic Polynomial
 