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?
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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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