Question

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

Answer 1

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.