Class IX Math NCERT Solutions For Polynomials Exercise– 2.1

Exercise– 2.1
1.  Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.
Ans. (i)   4x2 – 3x + 7
                ⇒ 4x2 – 3x + 7x°
                ∵ All the exponents of x are whole numbers.
                ∴ 4x2 – 3x + 7 is a polynomial in one variable.
         (ii)   
                 
                ∵ All the exponents of y are whole numbers.
                ∴  is a polynomial in one variable.
         
         
         (v)   x10 + y3 + t50
                ∵; Exponent of every variable is a whole number,
                ∴ x10 + y3 + t50 is a polynomial in x, y and t, i.e. in three variables.
2.  Write the co-efficients of x2 in each of the following:
         (i)   2 + x2 + x
         (ii)   2 – x2 + x3
         (iii)   
         (v)   
Ans. (i)   2 + x2 + x
                The co-efficient of x2 is 1.
         (ii)   2 – x2 + x3
                The co-efficient of x2 is (–1).
         (iii)   
                The co-efficient of x2 is 
         (iv)   
                
                ∴  The co-efficient of x2 is 0
3.  Give one example each of a binomial of degree 35, and of a monomial of degree 100.
Ans. (i)   A binomial of degree 35 can be: 3x35 – 4
         (ii)   A monomial of degree 100 can be: 
4.  Write the degree of each of the following polynomials:
         (i)   5x3 + 4x2 + 7x
         (ii)   4 - y2
         (iii)   
         (iv)   3
Ans. (i)   5x3 + 4x2 + 7x
                ∵ The highest exponent of x is 3.
                ∴ The degree of the polynomial is 3.
         (ii)   4 – y2
                ∵ The highest exponent of y is 2.
                ∴ The degree of the polynomial is 2.
         (iii)   
                ∵ The highest exponent of t is 1.
                ∴ The degree of the polynomial is 1.
         (iv)   3
                since, 3 = 3x°
                ∴ The degree of the polynomial 3 is 0.
5.  Classify the following as linear, quadratic and cubic polynomials:
         (i)   x2 + x
         (ii)   x – x3
         (iii)   y + y2 + 4
         (iv)   1 + x
         (v)   3t
         (vi)   r2
         (vii)   7x3
Ans. (i)   x2 +x
                ∵ The degree of x2 + x is 2.
                ∴ It is a quadratic polynomial.
         (ii)   x – x3
                ∵ The degree of x – x3 is 3.
                ∴ It is a cubic polynomial.
         (iii)   y + y2 + 4
                ∵ The degree of y + y2 + 4 is 2.
                ∴ It is a quadratic polynomial.
         (iv)   1 + x
                ∵ The degree of 1 + x is 1.
                ∴ It is a linear polynomial.
         (v)   3t
                ∵ The degree of 3t is 1.
                ∴ It is a linear polynomial.
         (vi)   r2
                ∵ The degree of r2 is 2.
                ∴ It is a quadratic polynomial.
         (vii)   7x3
                ∵ The degree of 7x3 is 3.
                ∴ It is a cubic polynomial.

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