Find how the polynomial behaves and the maximum number of turning points

Question

Polynomial: f(x) = -2(x+3)(x-2)³

A) the graph of f behaves like y = ____ for large values of | x |

B) determine the maximum number of of turning points on the graph of the function

thank you to anyone who helps!

Answer 1

A) f behaves like y = -2x⁴ for large values of |x|, since the polynomial behaves like the dominant term (the term with highest power) for large values of |x|.

B) The maximum number of turning polynomials is always the degree - 1, so in this case that will be 4 - 1 = 3.