Question

Find the quotient and the remainder when :
a³ − 5a² + 8a + 15 is divided by a + 1. verify your answer.

Answer 1

`"a"+1) overline("a"^3-5"a"^2+8"a"+15)("a"^2-6"a"+14`
          a³ + a²      
         −   −                        
       −6a² + 8a + 15 
       −6a2 − 6a  
       +       +                       
          14a + 15
          14a + 14                
                     1                  

∴ Quotient = a² − 6a + 14 and reminder = 1

Verification :

Dividiend = Quotient × Divisor + Reminder

= (a2 − 6a + 14) × (a + 1) + 1

= a³ − 6a² + 14a + a² − 6a + 14 + 1

= a³ − 5a² + 8a + 15 which is given