Give an example of the graph of a polynomial which has 4 zer

Give an example of the graph of a polynomial which has 4 zeros, none of which have odd multiplicity, and has the same end behavior as x^5.

Solution

4 zeros of even multiplicity
and same end behavior as x^5

Now, for a zero to have even multiplicity, it will hit the x-axis and then bounce right back.

Also, if all the zeros have even multiplicity, then the overall degree of equation will be even and it can never have an
end behavior similar to x^5

So, no such graph is possible