Use long division to simplify: `(3w^3-6w^2-27w+54)/(2w^2-4w-30)`  

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The expression `(3w^3 - 6w^2 - 27w + 54)/(2w^2 - 4w - 30)` has to be simplified.

`(3w^3 - 6w^2 - 27w + 54)/(2w^2 - 4w - 30)`

=> `(3(w^3 - 2w^2 - 9w + 18))/(2w^2 - 4w - 30)`

=> `(3(w^2(w - 2) - 9(w - 2)))/(2w^2 - 4w - 30)`

=> `(3(w^2 - 9)(w - 2))/(2w^2 - 4w - 30)`

=> `(3(w - 3)(w + 3)(w - 2))/(2w^2 - 4w - 30)`

=> `(3(w - 3)(w + 3)(w - 2))/(2(w^2 - 2w - 15))`

=> `(3(w - 3)(w + 3)(w - 2))/(2(w^2 - 5w + 3w - 15))`

=> `(3(w - 3)(w + 3)(w - 2))/(2(w(w - 5) + 3(w - 5)))`

=> `(3(w - 3)(w + 3)(w - 2))/(2(w + 3)(w - 5))`

=> `(3(w - 3)(w - 2))/(2(w - 5))`

The simplified form is `(3(w - 3)(w - 2))/(2(w - 5))`

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