Question 1137099

{{{f(x)=x^2*(x-4)^3*(5x+2)}}}

to find the zeroes of the polynomial just set {{{f(x)=0}}}; your polynomial is already written as a product of factors

{{{x^2*(x-4)^3*(5x+2)=0}}}

{{{x^2=0}}}=>{{{x=0}}}->multiplicity {{{2}}}

{{{(x-4)^3=0}}}=>{{{x=4}}}->  multiplicity {{{3}}}

{{{(5x+2)=0}}}=>{{{x=-2/5}}}->  multiplicity {{{1}}}