Question 1037195
{{{f(x)=x^3(x-5)^2(x+9)}}} is given in fully factored form.
The zeros are the values of {{{x}}} that make a factor (and hence the product function) zero.
They are:
{{{highlight(x=0)}}} , with multiplicity {{{highlight(3)}}} ,
because the factor {{{(x-0)=x}}} appears with the exponent {{{3}}} in the fully factored expression of {{{f(x)}}} ,
{{{highlight(x=5)}}} , with multiplicity {{{highlight(2)}}} ,
because the factor {{{(x-5)}}} appears with the exponent {{{2}}} in the fully factored expression of {{{f(x)}}} , and
{{{highlight(x=-9)}}} , with multiplicity {{{highlight(1)}}} ,
because the factor {{{(x-(-9))=(x+9)}}} appears with no exponent
(which is the same having {{{1}}} as the exponent)
in the fully factored expression of {{{f(x)}}} .