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The function y={x^3+8x^2+21x+18}/{x+2} can be simplified into the function y= Ax^2 + bx + c  with a point of discontinuity at x=D .What is the sum of the values of A, B, C, and D?

 Jul 30, 2019
 #1
avatar+10492 
+1

The function y={x^3+8x^2+21x+18}/{x+2} can be simplified into the function y= Ax^2 + bx + c  with a point of discontinuity at x=D .What is the sum of the values of A, B, C, and D?

https://free-picload.com/images/2019/07/30/213.jpg

laugh

 Jul 30, 2019
 #2
avatar+103148 
+2

y  = ( x^3 + 8x^2 + 21x + 18) / (x + 2)

 

Using polynomial division to find the other polynomial factor, we have

 

              x^2  + 6x  + 9

x + 2   [  x^3 + 8x^2  + 21x  + 18 ]

              x^3 + 2x^2  

              ____________________

                         6x^2 + 21x

                         6x^2 + 12x

                         ________________

                                       9x  + 18

                                       9x  + 18

                                      ________

 

 

Then  we have that   y  = ( x^3 + 8x^2 + 21x + 18) / (x + 2)  =   (x^2 + 6x + 9) (x + 2) / (x + 2) =

 

x^2 + 6x + 9

 

The discontinuity occurs at   x + 2  = 0 ⇒   x  =  -2  = D

And A  = 1   B  = 6    C  = 9

 

So   A  + B + C + D    =   14

 

Here is a graph of this :https://www.desmos.com/calculator/nnhk1oofs1

 

cool cool cool             

 Jul 30, 2019
 #3
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Thanks for the help!

 Jul 31, 2019

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