Find the Quotient and the Remainder When : A3 − 5a2 + 8a + 15 is Divided by a + 1. - Mathematics

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Sum

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

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Solution

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

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Chapter 11: Algebraic Expressions - Exercise 11 (D) [Page 146]

APPEARS IN

Selina Concise Mathematics Class 8 ICSE
Chapter 11 Algebraic Expressions
Exercise 11 (D) | Q 2.1 | Page 146

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