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

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Answer 1 · 2015-09-09T16:58:54

If you expand y you will get the following

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

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

$y=x^5(-3+12x^4/x^5+21x^3/x^5-102x^2/x^5-36x/x^5+216/x^5)$

As $x->+oo ,y->-oo$ and $x->-oo ,y->+oo$

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