Question 1012085

{{{x^3+ 4x ^2+ 5x}}}


 ={{{x(x^2+ 4x + 5)}}}


={{{x(x^2+ 4x + 5)}}}......use quadratic formula to find the roots of {{{x^2+ 4x + 5}}}


{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 


{{{x = (-4 +- sqrt( 4^2-4*1*5 ))/(2*1) }}} 


{{{x = (-4 +- sqrt( 16-20 ))/2 }}} 


{{{x = (-4 +- sqrt( -4 ))/2 }}} 


{{{x = (-4 +- 2i)/2 }}} 


{{{x = (-cross(4)2 +- cross(2)i)/cross(2) }}} 


{{{x = (2 +-i) }}}


roots: {{{x = (2 +i) }}} and {{{x = (2 -i) }}}


use their product rule and you have {{{(x+ (2 +i))}}} and {{{(x+(2 -i)) }}}


so, to continue with factoring, we have


={{{x(x+ (2 +i))(x+(2 -i))}}}


={{{x(x+ 2 +i)(x+2 -i)}}}