# How do you find the end behavior of y=-3(x-2)(x+2)^2(x-3)^2?

If you expand y you will get the following

$y = - 3 {x}^{5} + 12 {x}^{4} + 21 {x}^{3} - 102 {x}^{2} - 36 x + 216$

#### Explanation:

Now if we let x^5 be a common factor like that

$y = {x}^{5} \left(- 3 + 12 {x}^{4} / {x}^{5} + 21 {x}^{3} / {x}^{5} - 102 {x}^{2} / {x}^{5} - 36 \frac{x}{x} ^ 5 + \frac{216}{x} ^ 5\right)$

As $x \to + \infty , y \to - \infty$ and $x \to - \infty , y \to + \infty$