Question

what is the factorization of the trinomial below? x^2 - 12x + 35xA. (x-7)(x+5)B. x(x-7)(x+5)C. x(x-7)(x-5)D. (x^2-7)(x+5)

Answer 1

Given the trinomial below:

`x^3-12x^2+35x`

To factorize, we have

`\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}`

Hence, the factorization of the trinomial gives:

`x(x-7)(x-5)`

The correct option is C