Simplify using long division. (72 - 8x^2 + 4x^3 - 36x) / (x - 3)

Expert Answers
crmhaske eNotes educator| Certified Educator

First, order the numerator by degrees of x:


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^3-8x^2-36x+72)/(x-3) = 4x^2+4x-24` 


oldnick | Student

`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)=`


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