(A) Given That $f(x)=x^{6}-5 x^{5}+3 x^{4}+23 x^{3}-112 x^{2}+162 x-72$ Has 1 as a Zero of Multiplicity

Essay

(a) Given that $f(x)=x^{6}-5 x^{5}+3 x^{4}+23 x^{3}-112 x^{2}+162 x-72$ has 1 as a zero of multiplicity $2,-3$ as a single zero, and 4 as a single zero, find all other zeros of $f$ .
(b) Use the information from part (a) to sketch the graph of $f$ by hand. Give an end behavior diagram.