Answer:
The factor is : [tex]x(x+2)(x^{3}-2x^{2}-2)[/tex]
Step-by-step explanation:
Given expression is :
[tex]p(x)=x^{5}-4x^{3}-2x^{2}-4x =0[/tex]
Taking out x common factor we get
[tex]x^{4}-4x^{2}-2x-4=0[/tex]
Further applying rational root theorem we get
[tex](x+2)\frac{x^{4}-4x^{2}-2x-4}{x+2}[/tex]
Now we will divide [tex]\frac{x^{4}-4x^{2}-2x-4}{x+2}[/tex] and get
[tex]x^{3}+\frac{-2x^{3}-4x^{2}-2x-4}{x+2}[/tex]
[tex]x^{3}-2x^{2} +\frac{-2x-4}{x+2}[/tex]
[tex]\frac{-2x-4}{x+2}[/tex] = -2
The next factor becomes : [tex]x^{3}-2x^{2} -2[/tex]
Now clubbing all the factors we get the final answer:
[tex]x(x+2)(x^{3}-2x^{2}-2)[/tex]
