For what value of 'k' will (x + 2) be a factor of 3x3 + 4x2 + kx - 8?

By definition, if (x + 2) is a factor, then x = - 2 is a factor to the polynomial using the Remainder and Factor theorem.

Thus, we can say that the remainder when x = - 2 should be 0.

P (-2) = 0;

3 (-2) ³ + 4 (-2) ² - 2k - 8 = 0

3 (-8) + 16 - 2k - 8 = 0

-24 + 16 - 8 - 2k = 0

-16 - 2k = 0

-2k = 16

k = - 8

Thus, the value for k that will make (x + 2) a factor is k = - 8