Answer:
P(x) = (x - 1)(x + 2)(x - 3)(3x + 1)
Step-by-step explanation:
Since P(1) = 0 and P(- 2) = 0, then
(x - 1) and (x + 2) are factors of P(x)
(x - 1)(x + 2) = x² + x - 2 ← is also a factor of P(x)
dividing 3 - 5x³ - 17x² + 13x + 6 by x² + x - 2 gives
P(x) = (x - 1)(x + 2)(3x² - 8x - 3) = (x - 1)(x + 2)(x - 3)(3x + 1)
