What is the value of k such that x - 7 is a factor of f(x) = 2x3 - 13x2 - kx + 105? Show all computation and justify your answer.

2x³ - 13x² -kx + 105

since x - 7 is a factor, therefore x - 7 = 0 ; x = 7

Substitute the value for x in the equation.

i.e f(x) = 2x³ - 13x² -kx + 105

f(7) = 2(7)³ - 13(7)² - k(7) + 105

0 = 2(343) - 13(49) - 7k + 105

0 = 686 - 637 - 7k +105

0 = 154 - 7k

7k = 154

k = 154/7

k = 22

2x³ - 13x² -kx + 105

since x - 7 is a factor, therefore x - 7 = 0 ; x = 7