Question 1130201


 Grouping method and rational zeros' 

Grouping method:

{{{f(x)=x^3+3x^2-2x-6 }}}

{{{f(x)=(x^3+3x^2)-(2x+6 )}}}

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

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

{{{f(x)=(x^2-(sqrt(2))^2)(x+3 )}}}

{{{f(x)=(x-sqrt(2))(x+sqrt(2))(x+3 )}}}


rational zeros' method: square both sides

{{{0=sqrt(x^3+3x^2-2x-6) }}}

{{{0=sqrt((x + 3) (x^2 - 2))}}}

{{{0=sqrt(x + 3) sqrt(x^2 - 2)}}}

roots:

if {{{0=sqrt(x + 3) }}}->{{{x+3=0}}}->{{{x=-3}}}

if {{{0= sqrt(x^2 - 2)}}}->{{{x^2 - 2=0}}}->{{{x^2 = 2}}}->{{{x = sqrt(2)}}} or {{{x = -sqrt(2)}}}