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=?

Algebra ->  Algebra  -> Customizable Word Problem Solvers  -> Geometry -> 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=?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

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(6938) 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:


3x%5E3%2B2x%5E2%2Bx%2B20+=+A%2BB%28x-1%29%2BC%28x-1%29%28x-2%29%2BD%28x-1%29%28x-2%29%28x-3%29

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


Substitute 1 for x in the above:

3%281%29%5E3%2B2%281%29%5E2%2B%281%29%2B20+=+A%2BB%281-1%29%2BC%281-1%29%281-2%29%2BD%281-1%29%281-2%29%281-3%29

3%2B2%281%29%2B%281%29%2B20+=+A%2BB%281-1%29%2BC%281-1%29%281-2%29%2BD%281-1%29%281-2%29%281-3%29

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

---

3x%5E3%2B2x%5E2%2Bx%2B20+=+A%2BB%28x-1%29%2BC%28x-1%29%28x-2%29%2BD%28x-1%29%28x-2%29%28x-3%29

Now substitute 2 for x in the above:

3%282%29%5E3%2B2%282%29%5E2%2B%282%29%2B20+=+A%2BB%282-1%29%2BC%282-1%29%282-2%29%2BD%282-1%29%282-2%29%282-3%29

3%288%29%2B2%284%29%2B%282%29%2B20+=+A%2BB%281%29%2BC%281%29%280%29%2BD%281%29%280%29%28-1%29

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