PLEEZZ HELP AND SHOW WORK!determine the zeros of :f(x)=x^4-x^3+7x^2-9x-18

Question

anonymous · Answer

ahhhh i need an answer fast
 :((

turingtest · Answer

well sorry, but this problem is going to take a bit of time to solve...

anonymous · Answer

as long as you can get i i will love you forever! :P

turingtest · Answer

by the rational root theorem we should first just try some factors of 18
try$$\pm1,\pm2,\pm3,\pm6,\pm18$$try them out; are any of those numbers zero's of the polynomial?

anonymous · Answer

-1 is one of the roots then i can factor out (x+1)

$$x^4-x^3+7x^2-9x-18=x^4+x^3-2x^3-2x^2+9x^2-9x-18\=x^3(x+1)-2x^2(x+1)+9(x^2-x-2)=x^3(x+1)-2x^2(x+1)+9(x+1)(x-2)\ =(x+1)(x^3-2x^2+9x-18)$$

try to doing same with poynomial with degree 3

anonymous · Answer

(x-2)****