NCERT Class 9 Mathematics

38 MATHEMATICS

Let us consider some more examples.

Example 7 : Divide the polynomial 3x^4 – 4x^3 – 3x –1 by x – 1.

Solution : By long division, we have:

3 x^3 – x^2 – x – 4

x – 1 3 x (^4) – 4x (^3) – 3x – 1
(^) – 3 x^4 –+ 3 x^3

• x^3 – 3 x – 1


• 
  
  
  
  • 
    
  
  
  
  

x^3 +

x^2

• x^2 – 3x – 1


• 
  
  
  
  • x^2 +– x
  
  
  
  


• 4x – 1


• 
  
  
  
  • 
    
  
  
  
  

4 x +

4

– 5

Here, the remainder is – 5. Now, the zero of x – 1 is 1. So, putting x = 1 in p(x), we see
that

p(1) = 3(1)^4 – 4(1)^3 – 3(1) – 1

= 3 – 4 – 3 – 1

= – 5, which is the remainder.

Example 8 : Find the remainder obtained on dividing p(x) = x^3 + 1 by x + 1.

Solution : By long division,

x^2 – x + 1

x + 1 x^3 + 1

(^) – x^3 +– x^2

• x^2 + 1


• 
  
  
  
  • 
    
  
  
  
  

x^2 –

+

x

x + 1

x +

1

0