Find a polynomial of least possible degree having the graph

Find a polynomial of least possible degree having the graph shown. Use a leading coefficient of 1 or -1 f(x)= (Simplify your answer.)

Solution

Here the zeroes are at x=-1,x=4 and the degree is even since it starts and end in the same direction.

f(x)-(x+1)²(x-4)² = -x⁴+6x³-x²-24x-16