Question 1198584


 {{{x^5-13x^3+36x=0}}}..........factor

{{{x (x^4 - 13x^2 + 36) = 0}}}


factor {{{x^4 - 13x^2 + 36}}}:

let {{{x^2=u}}}

{{{u^2 - 13u + 36=u^2 - 4u -9u+ 36=(u^2 - 4u) -(9u- 36)=u(u - 4) -9(u- 4)=(u -9)(u- 4)}}}

Substitute back {{{x^2=u}}}

{{{(x^2 -9)(x^2- 4)=(x - 3) (x - 2) (x + 2) (x + 3)}}}

so,

  {{{x^5-13x^3+36x=x(x - 3) (x - 2) (x + 2) (x + 3) }}}

solutions:

{{{x=0}}}
{{{x=3}}}
{{{x=2}}}
{{{x=-2}}}
{{{x=-3}}}


answer:
A)