Question

can x2-1 be remainder while dividing x4-3x2-5x-9 by x2+3? justify

Answer 1

Given : x⁴-3x²-5x-9 divided by x²+3

To Find : can x²-1 be remainder

Solution:

Degree of remainder is always less than the degree of divisor

Hence  x²-1  can not be remainder if divisor is x²+3  

as x² -  1  = 1* ( x²  + 3)  - 4

Hence remainder will be  = - 4    

                 x²-6

x²+3  _|  x⁴-3x²-5x-9   |_

               x⁴ +3x²

           ________

                    -6x² - 5x - 9

                    -6x²         -18

                   _________

                               -5x + 9

Remainder is -5x + 9

x²-1  can not be remainder if divisor is x²+3  

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