plz help

Given that x=2 is a root of p(x)=x^4-3x^3-18x^2+90x-100, find the other roots (real and nonreal).

Hello Guest!

$x_1=2$

$(x^4-3x^3-18x^2+90x-100)$ : $(x-2)$=  $x^3 - x^2 - 20 x + 50$

 $\underline{x^4-2x^3}$

          $-x^3-18x^2$

         $\underline{-x^3\ +\ 2x^2}$

                   $-20x^2+90x$

                  $\underline{-20x^2+40x}$

                                   $50x-100$

                                   $\underline{50x-100}$

                                                   0

$x_2=-5$

   $(x^3 -\ x^2 - 20 x + 50)$ : $(x+5)$ =  $x^2-6x+10$ 

    $\underline{x^3+5x^2}$

          $-6x^2-20x$

          $\underline{-6x^2-30x}$

                         $10x+50$

                         $\underline{ 10x+50}$

                                       0

  $x^2-6x+10=0$ 

  $x=3\pm \sqrt{9-10}$

 $x_3=3+i\\ x_4=3-i$

  !