Question 764822
{{{f(x) = x^3 + 5x^2 + x + 5}}}...group terms


{{{f(x) =( x^3  + x) + (5x^2+ 5)}}}...factor

{{{f(x) =x( x^2  + 1) + 5(x^2+ 1)}}}

{{{f(x) =(x + 5)(x^2+ 1)}}}

solutions: use zero product rule

{{{(x + 5)(x^2+ 1)=0}}}

if {{{(x + 5)=0}}} => {{{x=-5}}}.....one real zero, means the line crosses {{{x-axis}}} at ({{{-5}}},{{{0}}}) 

if {{{x^2+ 1=0}}} => {{{x^2=-1}}}.....=> {{{x=sqrt(-1)}}}=> {{{x=i}}} and {{{x=-i}}}...two imaginary zeros 


{{{ graph( 600, 600, -10, 10, -10, 25, (x + 5)(x^2+ 1)) }}}