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?

Guest Jul 30, 2019

#1**+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?

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Omi67 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

CPhill Jul 30, 2019