Use the leading coefficient test to indicate the end behavior of the graph of the polynomial function. Indicate the zero of the function.
f(x)=-2x^3(x+5)^4(x-3)^2
I need help with this problem. I don't even know where to begin.
So the degree of f(x) is p and the lead terms will be of the form
$\displaystyle -2x^9$ (why?)
as $\displaystyle x \to -\infty \mbox{ f(x) } \to \infty$
as $\displaystyle x \to \infty \mbox{ f(x) } \to -\infty$
again why?
Since it is already factored the zero's are$\displaystyle x=0,-5,3$
Good luck.
What would happen if we multiplied out the whole thing?
Lets look at one part
$\displaystyle (x+5)^4=(x+5)(x+5)(x+5)(x+5)$
We distributedthe whole thing out (we don't need to) to find the highest power of x .
Well to get that terms we would multiply x by x by x by x $\displaystyle =x^4$
$\displaystyle
f(x)=-2x^3 \cdot \underbrace{(x+5)^4}_{x^4} \cdot \underbrace{(x-3)^2}_{x^2}
$
so our lead term will be $\displaystyle -2x^9$