Question 1110636
This response is not a full solution but only an approach to begin.

Try to sketch your graph's description and you will see the polynomial is degree 4; and since decreasing when unbound to the left and also decreasing when unbound to the right, lead coefficient is negative.  You may have something LIKE {{{y=-ax^4+bx^3+cx^2+dx+e}}};


One of the zeros will be of multiplicity 2.


You may want to start with something in factorized form first...


You might find with the help of a graphing tool that   {{{y=-(x+2)(x-1)^2*(x-3)}}} give the right shape and the right zeros, but not yet the right y-intercept, but you can find it by using some "a" as the factor and let x=0 to find "a".