One factor of x³ - kx² + 11x - 6 is x - 1. The value of k is :

1. -6

2. 12

3. 6

4. -12

By factor theorem,

If x - a is a factor of polynomial f(x), then remainder f(a) = 0.

Given,

x - 1 is a factor of 8x² - 7x + m.

⇒ x - 1 = 0

⇒ x = 1.

Substituting x = 1, in x³ - kx² + 11x - 6 remainder will be zero.

⇒ 1³ - k(1)² + 11(1) - 6 = 0

⇒ 1 - k + 11 - 6 = 0

⇒ 6 - k = 0

⇒ k = 6.

Hence, Option 3 is the correct option.