Question

Use the rational zero theorem to list all possible rational zeros for the given function
f(x)=x^3-4x^2-19x-14

Answer 1

-2, -1, 7

Answer 2

try x = ±1, ±2, and ± 7
f(1) = 1 - 4 - 19 - 14 ≠ 0
f(-1) = -1 - 4 + 19 - 14 = 0
ahhh, so (x+1) is a factor

using algebraic division
x^3-4x^2-19x-14 = 0
(x+1)(x+2)(x-7) = 0
so x = -1, -2 or 7