SOLUTION: If P(x)=3x^3+2x^2+x+20 and we write P(x) in the form P(x)=A+B(x-1)+C(x-1) (x-2)+D(x-1)(x-2)(x-3) A=? and B=?

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Question 210907: If P(x)=3x^3+2x^2+x+20 and we write P(x) in the form P(x)=A+B(x-1)+C(x-1) (x-2)+D(x-1)(x-2)(x-3) A=? and B=?
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
If P(x)=3x^3+2x^2+x+20 and we write
P(x) in the form P(x)=A+B(x-1)+C(x-1) (x-2)+D(x-1)(x-2)(x-3) A=? and B=? 

Set both expressions for P(x) equal to each other:




Choose values for x that will cause some of those expresions
in parentheses to become 0.


Substitute 1 for x in the above:





3%2B2%2B1%2B20+=+A%2BB%280%29%2BC%280%29%28-1%29%2BD%280%29%28-1%29%28-2%29

26+=A

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Now substitute 2 for x in the above:





24%2B8%2B2%2B20+=+A%2BB

54=A%2BB

And since A=26, substituting:

54=A%2BB

54=26%2BB

28=B

So A=2 and B=28

Edwin