IX Std Term I - Chapter 3- Ex 3.3

Exercise 3.3

 

1.      Find the quotient and remainder of the following division.

(1)   (5x³ - 8x² + 5x - 7) ÷ (x - 1)

Solution:

     

                       5x² – 3x + 2

________________

  x – 1| 5x³ - 8x² + 5x – 7                           

                    |5x³ -  5x²
                    |-     +
                    |------------------------
                    |       - 3x² + 5x
                    |       - 3x² + 3x
                    |       +       -
                    |------------------------
                    |                  2x – 7
                    |                  2x – 2
                    |                 -     +
                    |------------------------
                    |                       - 5      

 

Quotient = 5x² – 3x + 2

Remainder = - 5

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(2)   (2x² -  3x - 14) ÷ (x + 2)

Solution:

(i)                  2x²/x = 2x

(ii)               2x(x + 2) = 2x² +4x

(iii)             -7x/x = -7

(iv)             -7(x+2) = -7x – 14

     

2x - 7             ___________

 

        x+2| 2x² - 3x – 14           
              | 2x² +4x
              |-      -
              |--------------------
              |        -7x – 14
              |        -7x – 14
              |        +     +
              |--------------------
              |                 0

Quotient = 2x - 7

Remainder = 0

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(3)   (9 + 4x + 5x² +  3x³ ) ÷ (x + 1)

Solution:

Writing the given polynomial in descending order, we get

(3x³ + 5x² + 4x + 9) ÷ (x + 1)

(i)                 3x3/x = 3x2 (ii)               3x2(x+ 1) = 3x3 + 3x2 (iii)             2 x2/x = 2x (iv)             2x(x + 1) = 2 x2 + 2x (v)               2x/x = 2 (vi)             2(x + 1) = 2x + 2                       3x2 + 2x + 2                    ______________

            x + 1| 3x³ + 5x² + 4x + 9
                      | 3x³ + 3x²
                     | -     -
                     |-------------------------
                     |           2x² + 4x
                     |           2 x² + 2x
                     |           -       -
                     |-------------------------
                     |                      2x + 9
                     |                      2x + 2
                     |                     -     -
                     |-------------------------
                     |                             7
 
  
           Quotient = 3x² + 2x + 2

Remainder = 7

        ---------------------------------------------------------------------------------------------------------

     (4)   (4x³ -  2x² +  6x +  7) ÷ (3 + 2x)

Solution:

Writing the given polynomials in descending order, we get

(4x³ - 2x² +  6x +  7) ÷ (2x + 3)

(i) 4x³/2x = 2x²

(ii) 2x²(2x + 3) = 4x³ + 6x²

(iii) - 8x²/2x = - 4x

(iv) – 4x(2x + 3) = - 8x² – 12x

(v) 18x/2x = 9

(vi) 9(2x + 3) = 18x +27

 

          

2x2 – 4x + 9                     ________________

            2x + 3| 4x³ - 2x² +  6x +  7
                      | 4x³ + 6x²
                      |-      -
                      |-----------------------------
                      |        - 8x² + 6x
                      |        - 8x² – 12x
                      |        +      +    
                      |-----------------------------
                      |           18x + 7            
                      |                     18x +27
                      |           -       -  
                      |-----------------------------
                      |                            - 20
                         

Quotient = 2x² – 4x + 9

Remainder = - 20

           -----------------------------------------------------------------------------------------------------------

(5)   ( -18 - 9x + 7x² ) ÷ (x - 2)

Solution:

Writing the given polynomial in descending order, we get

             (7x² – 9x – 18) ÷ (x – 2)
 

(i) 7x²/x = 7x

(ii) 7x(x – 2) = 7x² – 14x

(iii) 5x/x = 5

(iv) 5(x – 2) = 5x - 10

 

7x + 5

                    ____________
            x – 2| 7x² – 9x – 18
                    | 7x² – 14x
                    |-      +
                    |---------------------
                    |         5x - 18  
                    |         5x - 10     
                    |        -     +
                    |----------------------
                    |              - 8
            

Quotient = 7x + 5

Remainder = - 8

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