Solution:
Given the trinomial below:
[tex]x^3-12x^2+35x[/tex]
To factorize, we have
[tex]\begin{gathered} x^3-12x^2+35x \\ factor\text{ out the common terms,} \\ x(x^2-12x+35) \\ factorize\text{ the expression in parentheses, } \\ x(x^2-7x-5x+35) \\ x(x(x-7)-5(x-7)) \\ thus,\text{ we have} \\ x(x-5)(x-7) \end{gathered}[/tex]
Hence, the factorization of the trinomial gives:
[tex]x(x-7)(x-5)[/tex]
The correct option is C
