Question 696139: Given the identity Ax^3+x^2-2x-3=(3x+B)(x-1)(x+2)+C(x-1)+D , find the values of the constants A,B,C and D. Hence or otherwise, find the remainder when Ax^3+x^2-2x-3 is divided by x–1.
Answer by MathTherapy(10557)   (Show Source):
You can put this solution on YOUR website! Given the identity Ax^3+x^2-2x-3=(3x+B)(x-1)(x+2)+C(x-1)+D , find the values of the constants A,B,C and D. Hence or otherwise, find the remainder when Ax^3+x^2-2x-3 is divided by x–1.
 ----- Rearranging terms
From the above, we can see that:
 -------- 
 ------  ------  ----- 
 -----  ----  ----- 
 ----- Substituting – 2 for B
C = 4 + 2, or 
 ----- Substituting – 2 for B, and 6 for C
D = - 3 + 2, or 
With  ,  becomes:  , and when divided by x – 1, we have a remainder, or f(1) =  , or  , or 
You can do the check!!
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