[tex]Answer: \\ f(x) = k {x}^{3} - 8 {x}^{2} - x + 3k + 1 \\ \Rightarrow f(2) = k {2}^{3} - 8 {2}^{2} - 2 + 3k + 1 = 0 \\ \Leftrightarrow 8k - 32 - 2 + 3k + 1 = 0 \\ \Leftrightarrow 11k - 33 = 0 \\ \Leftrightarrow 11k = 33\Leftrightarrow k = 3 \\ \Rightarrow f(x) = 3 {x}^{3} - 8 {x}^{2} - x + 10 \\ Factored form:f(x) = (x + 1)(x - 2)(3x - 5) \\ Zeros: - 1,2, \frac{5}{3} [/tex]
