Question

question 40 of 40
what are the zeros of the polynomial function
f(x) = x³ - 5x² - 6x?

a. x = -3, x = 0, and x = 2
b. x = -2, x = 0, and x = 3
c. x = -1, x = 0, and x = 6
d. x = -6, x = 0, and x = 1

Explanation:

Step1: Factor out common term

$F(x) = x(x^2 - 5x - 6)$

Step2: Factor quadratic expression

$x^2 -5x -6 = (x-6)(x+1)$

Step3: Set factors to zero

$x=0$, $x-6=0$ → $x=6$, $x+1=0$ → $x=-1$

Answer:

C. x = -1, x = 0, and x = 6