An even function has 3 distinct roots and end behaviours where f(x) -> - infinity as x-> +- infinity. State one possible equation for this even function, and justify your choices.

Answer 1

Any ideas on any of these?
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Answer 2

Here I come to the rescue: P(x) = (x^2+1)(x+1)(x-1)

Answer 3

almost -- except you got the end-behavior sign wrong.
and your p(x) only has two distinct real roots, since (x^2+1) has no real roots.
Try p(x) = -x^2 (x-1)(x+1)