Answer:
[tex]=-\left(x-1\right)\left(x^4-6x^3-6x^2-14x-5\right)[/tex]
Step-by-step explanation:
Factor out comon Term -1
[tex]=-\left(x^5-7x^4-8x^2+9x+5\right)[/tex]
Factor [tex]x^5-7x^4-8x^2+9x+5:\quad \left(x-1\right)\left(x^4-6x^3-6x^2-14x-5\right)[/tex]
[tex]x^5-7x^4-8x^2+9x+5[/tex]
Use the rational root theorem
[tex]a_0=5,\:\quad a_n=1[/tex]
The dividers of [tex]a_{0}[/tex]: 1, 5, The dividers of [tex]a_n[/tex]: 1
Therefore, check the following rational numbers: ±[tex]\frac{1,\:5}{1}[/tex]
[tex]\frac{1}{1}[/tex] is a root of the expression, so factor out [tex]x-1[/tex]
[tex]=\left(x-1\right)\frac{x^5-7x^4-8x^2+9x+5}{x-1}[/tex]
[tex]\frac{x^5-7x^4-8x^2+9x+5}{x-1}=x^4-6x^3-6x^2-14x-5[/tex]
[tex]=x^4-6x^3-6x^2-14x-5[/tex]
[tex]=-\left(x-1\right)\left(x^4-6x^3-6x^2-14x-5\right)[/tex]
