Consider the polynomial function Px x3 2x2 5x 6 verify t

Consider the polynomial function P(x) = x^3 + 2x^2 - 5x - 6 verify that x=2 is a zero and factor P(x) completely. Solve the inequality P(x) greaterthanorequalto 0.

Solution

P(x) = x^3 + 2x^2 - 5x - 6

P(x) = (x - 2)(x + 1)(x + 3)

Thus x = 2 is zero and factor P(x) completely.

b) P(x) = x^3 + 2x^2 - 5x - 6 >= 0

(x - 2)(x + 1)(x + 3) > = 0

x > = 2, x > = -1, x >= -3