Chapter 2: Polynomials

EXERCISE = 2.1

1. Which of the following expressions are polynomials in one variables and which are not ?

      State reasons for your answer .

(i)  4x2-3x+7       (ii)   y2+2     (iii)  3t+t2    (iv)  y+2y     (v) x10+y3+t50 

Solution :  (i)  4x2-3x+7 is a polynomial in the variable x .      

     (ii)   y2+2  is a polynomial in the variable y .  

     (iii)  3t+t2  is not a polynomial in the variable t . 

     (iv)  y+2y  is not a polynomial in the variable y .  

     (v) x10+y3+t50 is not a polynomial in the three variable .

2. Write the coefficients of x2 in each of the following :

    (i)  2+x2+x      (ii)  2-x2+x3    (iii)  π2x2+x        (iv)  2x-1

Solution: (i)  2+x2+x   

                 The coefficients of x2 is 1 .

 (ii)  2-x2+x3 

          The coefficients of x2 is -1 .

 (iii)  π2x2+x     

The coefficients of x2 is  π2 .

   (iv)  2x-1 

 The coefficients of x2 is 0 .

3. Give one example each of a binomial of degree 35 and of a monomial of degree 100 .

Solution : The example of a binomial of degree 35 is x35+7 

             and  the example of a monomial of degree 100 is x100 .

4. Write the degree of each of the following polynomials :

          (i)  5x3+4x2+7x        (ii)  4-y2       (iii)  5t-7   (iv)  3

Solution : (i)  5x3+4x2+7x    

      The highest power of the variable is 3 . So , the degree of the polynomial is 3 .

  (ii)  4-y2   

     The highest power of the variable is 2 . So , the degree of the polynomial is 2 .

   (iii)  5t-7

    The highest power of the variable is 1 . So , the degree of the polynomial is 1 .

  (iv)  3=3x0 

      The exponent of x is 0 . So , the degree of the polynomial is 0 .