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Find the Quotient and the Remainder When : 3x4 + 6x3 − 6x2 + 2x − 7 is Divided by X − 3. Verify Your Answer. - Mathematics

Sum

Find the quotient and the remainder when :
3x4 + 6x3 − 6x2 + 2x − 7 is divided by x − 3. verify your answer.

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Solution

`-"x"-3)overline(3"x"^4+6"x"^3-6"x"^2+2"x"-7)(3"x"^3+15"x"^2+39"x"+119`
                3x4 − 9x3
                −    +                           
               15x3 − 6x2 + 2x − 7   
               15x3 − 45x2    
                −     +                         
               39x2 + 2x − 7
               39x2 − 117x  
               −      +                           
               119x − 7
               119x − 357         
                       −   +       
                   350

∴ Quotient = 3x3 + 15x2 + 39x + 119 and reminder = 350

Verification : 

Dividend = Quotient × Divisor + Reminder

= (3x3 + 15x2 + 39x + 119) (x − 3) + 350

= 3x4 + 15x3 + 39x2 + 119x − 9x3 − 45x2 − 117x − 357 + 350

= 3x4 + 6x3 − 6x2 + 2x − 7 which is given

Concept: Division of Algebraic Expressions - Dividing a Polynomial by a Polynomial
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APPEARS IN

Selina Concise Mathematics Class 8 ICSE
Chapter 11 Algebraic Expressions
Exercise 11 (D) | Q 2.2 | Page 146
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