select all of the zeros of f(x)=x^3-4x^2-9x-36.
A x=3
B x=4
C x=2
D x=-4
E x=-3
F x=-2
To find the zeros of the function f(x), we need to find the values of x for which f(x) equals zero.
We can try plugging in each answer choice into the function and see if it equals zero. If it does, then that value is a zero of the function.
A) f(3) = 3^3 - 4(3^2) - 9(3) - 36 = 27 - 36 - 27 - 36 = -72, so x = 3 is not a zero of the function.
B) f(4) = 4^3 - 4(4^2) - 9(4) - 36 = 64 - 64 - 36 - 36 = -72, so x = 4 is not a zero of the function.
C) f(2) = 2^3 - 4(2^2) - 9(2) - 36 = 8 - 16 - 18 - 36 = -62, so x = 2 is not a zero of the function.
D) f(-4) = (-4)^3 - 4((-4)^2) - 9(-4) - 36 = -64 - 64 + 36 - 36 = -128, so x = -4 is not a zero of the function.
E) f(-3) = (-3)^3 - 4((-3)^2) - 9(-3) - 36 = -27 - 36 + 27 - 36 = -72, so x = -3 is a zero of the function.
F) f(-2) = (-2)^3 - 4((-2)^2) - 9(-2) - 36 = -8 - 16 + 18 - 36 = -42, so x = -2 is not a zero of the function.
Therefore, the zeros of f(x) = x^3 - 4x^2 - 9x - 36 are x = -3, which corresponds to answer choice E.