What is the condition for a linear expression to be a factor of a polynomial (that is, how do you know when a linear expression is a factor of a polynomial)? (b). Given the polynomial P(x) = 6x³ + 11x² - 5x -12 which of the following linear expressions are factors of P(x) (show working to support your answer): (i). 3x + 4 (ii). x + 4 (iii). 2x + 3 (iv). x - 1 (c). Based on your answers from part (b), above:

(i). Find three different quadratic expressions which are factors of P(x). (ii). Express/state (write down) P(x) in terms of its linear factors.