polynomial function problem

Question

given : p(x) = x(x+5)(x+3)(x-2)²

what degree is the polynomial function?

what is the end behavior of p(x)?

Answer 1

Degree--

Expanding the expression:

p(x) = x (x + 5) (x + 3) (x - 2)^2 = x^5 + 4 x^4 - 13 x^3 - 28 x^2 + 60 x

Because 5 is the largest degree of any term (x^5), then 5 is the degree.

End Behavior--

By checking the graph/assessing the limits, we see:

As x --> +∞, p(x) --> +∞

As x --> -∞, p(x) --> -∞

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Hope this helps!