Question

Find without actual division,the remainder if ................................. ?Answer pls

Answer 1

hey guy your answer is -1
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Answer 2

Sol : Let p ( x ) = 4x^5 - 7x^3 - x^3 + 8,

         and f ( x ) = 2x + 3.

Zero of f ( x ) , 2x + 3 = 0

                       2x = -3

                   So, x = -3 / 2.

By Remainder  theorem ,

p ( x ) = 4 x^5 - 7x^3 - x^2 + 8

p ( -3/2 ) = 4 ( -3 / 2 )^5 - 7 ( -3 / 2 )^3 - ( -3 / 2 )^2 + 8

p ( -3 / 2 ) = 4 ( - 243 / 32 ) - 7 ( - 27 / 8 ) - ( 9 / 4 ) + 8


p ( -3/2 ) = ( -243 / 8 ) +  ( 189 / 8 ) - ( 9 / 4 ) + 8

                       -243 + 189 - 18 + 64
p (-3/2) = ---------------------------------------
                                     8

                    -261 + 253
p ( -3/2) = -----------------------
                          8

p ( -3/2) = -8 / 8 = -1.

So, when ( 4x^5 - 7x^3 - x^2 + 8 ) is divided by ( 2x + 3 ) , then remainder is   ( -1 ).

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