SOLUTION: Please help me to find constants a,b and c given that: 2x^3 - x^2 + 6 = (x-1)^2 (2x + a) + bx + c, for all x

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Question 1160951: Please help me to find constants a,b and c given that:
2x^3 - x^2 + 6 = (x-1)^2 (2x + a) + bx + c, for all x

Found 2 solutions by Edwin McCravy, solver91311:
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
Since it is true for ALL x, let's choose x=0:



for x=0














So replace c by 6-a

in





Again, since it is true for ALL x, let's choose x=1:















So substitute a+1 for b in





Again, since it is true for ALL x, let's choose x=-1:















Substitute in





Substitute in





So a=3, b=4, c=3.

Edwin


Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!













Equate the coefficients:







Solve the 3X3 system for , , and


John

My calculator said it, I believe it, that settles it


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