Simplify using long division.

(72 - 8x^2 + 4x^3 - 36x) / (x - 3)

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First, order the numerator by degrees of x:

`(4x^3-8x^2-36x+72)/(x-3)`

Now we can start the long divison. In order to display this clearly, I will not use the equation editor so that I can line everything up.

4x^2+4x -24

x-3| 4x^3- 8x^2-36x+72

4x^3-12x^2

4x^2-36x

4x^2-12x

-24x+72

-24x+72

0

Therefore:

` ` `(4x^3-8x^2-36x+72)/(x-3) = 4x^2+4x-24`

`72-8x^2+4x^3-36x` =`8(9-x^2)+4x(x^2-9)=`

`4x(x^2-9)- 8(x^2-9)=(4x-8)(x^2-9)=`

`=2(x-4)(x+3)(x-3)`

So: `(72-8x^2+4x^2-36x)/(x-3)=(2(x-4)(x+3)(x-3))/(x-3)` `=2(x-4)(x+3)`

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