Respuesta :
The given function is,
[tex]6x^3-7x^2-9x-2[/tex]polynomial equation with integer coefficient
[tex]a_nx^n+a_{n-1}x^{n-1}+\ldots+a_0[/tex][tex]\begin{gathered} ifa_{0\text{ }},a_1\text{ are integres and if the rational root exist we can find by } \\ \text{checking all the numbers produced by } \\ \pm\frac{\: dividers\: of\: a_0}{dividers\: of\: a_n} \\ \end{gathered}[/tex]Here,
[tex]a_0=2,\: \quad a_n=6[/tex]The divisors of
[tex]\begin{gathered} a_0\colon\quad 1,\: 2 \\ a_n\colon\quad 1,\: 2,\: 3,\: 6 \end{gathered}[/tex]The rational roots are,
[tex]\pm\frac{1,\:2}{1,\:2,\:3,\:6}[/tex]validate the roots by plugging them into the function
[tex]6x^3-7x^2-9x-2=0[/tex][tex]x=2,x=-\frac{1}{2},x=-\frac{1}{3}[/tex]The factor of the equation are,
[tex]\begin{gathered} (x-2)\mleft(2x+1\mright)\mleft(3x+1\mright) \\ \end{gathered}[/tex]