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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
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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
#2
+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   Jul 30, 2019