If x2 + kx + 18 is factorable, what are the possible values of k?

Assume that x² + kx + 18 if factorable.

The factors of 18 are

(1 x 18); (2 x 9); (3 x 6).

If we use (1, 18) as factors, then

(x - 1) (x - 18) = x² - 19x + 18 = > k = - 19

or

(x + 1) (x + 18) = x² + 19x + 18 = > k = 19

If we use (2,9) as factors, then

(x - 2) (x - 9) = x² - 11x + 18 = > k = - 11

or

(x + 2) (x + 9) = x² + 11x + 18 = > k = 11

If we use (3, 6) as factors, then

(x - 3) (x - 6) = x² - 9x + 18 = > k = - 9

or

(x + 3) (x + 6) = x² + 9x + 18 = > x = 9

Answer:

The possible values of k are - 9,+9, - 11, + 11, - 19, + 19.