Question 1025457
A) When {{{x=0}}},
{{{f(0)=(-5)(4)(-3)=60}}}
B) {{{x-5=0}}}
{{{x=5}}}
and
{{{x+4=0}}}
{{{x=-4}}}
and
{{{x-3=0}}}
{{{x=3}}}
C) Break up the number line into regions using the x-intercepts,
Region 1 : ( {{{-infinity}}},{{{-4}}})
Region 2 : ({{{-4}}},{{{3}}})
Region 3 : ({{{3}}},{{{5}}})
Region 4 : ({{{5}}},{{{infinity}}})
Pick a point in each region and test the function to see if its greater than or less than zero.
Region 1 : {{{x=-5}}}
{{{f(-5)=(-5-5)(-5+4)(-5-3)=(-10)(-1)(-8)=-80}}}
Region 2 : {{{x=0}}}
{{{f(0)=60}}}
Region 3 : {{{x=4}}}
{{{f(4)=(4-5)(4+4)(4-3)=(-1)(8)(1)=-8}}}
Region 4 : {{{x=6}}}
{{{f(6)=(6-5)(6+4)(6-3)=(1)(10)(3)=30}}}
So then,
 ( {{{-infinity<x<-4}}}) , {{{f(x)<0}}}
({{{-4<x<3}}}) {{{f(x)>0}}}

 ({{{3<x<5}}}), {{{f(x)<0}}}

({{{5<x<infinity}}}), {{{f(x)>0}}}