Factor -2 out:
[tex]-2(x^3-7x^2+12x-10)[/tex]The divisors of 10 are:
[tex]1,2,5,10[/tex]Therefore, the possible rational roots of the:
[tex]x^3-7x^2+12x-10[/tex]are:
[tex]\begin{gathered} x=\pm1 \\ x=\pm2 \\ x=\pm5 \\ x=\pm10 \end{gathered}[/tex]so:
This gives x - 5 as all linear factors:
[tex]-2\frac{(x-5)(x^3-7x^2+12x-10)}{(x-5)}[/tex]Therefore, the binomial factor is:
[tex](x-5)[/tex]