Question

Find the remainder when x^3 + 3x^2 + 3x +1 is divided by (i) x - 1/2 & (ii) 5 + 2x
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Answer 1

Apply remainder theorem 
=>x – 1/2 =0 
=> x =  1/2 
Replace x by  1/2 we get 
=>x3+3x2 + 3x + 1
=>(1/2)3 + 3(1/2)2 + 3(1/2) + 1
=> 1/8 + 3/4 + 3/2 + 1
Add the fraction taking LCM of denominator we get 
=>(1 + 6 + 12 + 8)/8 
=>27/8
Remainder is 27/8 

Apply remainder theorem 
=>5+2x =0 
=> 2x = - 5
=> x = - 5/2 
Replace x by – 5/2 we get 
=>x3+3x2 + 3x + 1
=>(-5/2)3 + 3(-5/2)2 + 3(-5/2) + 1
=> -125/8  + 75/4 – 15/2 + 1
Add the fraction taking LCM of denominator 
=>(-125 + 150  - 60 + 8 )/125
=> -27/8
Remainder is -27/8

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