Question

Consider polynomial function f(x) = (x+ 1)(x−2)(x−3).

(a) Find all zeros.
(b) The zeroes divide R into a few open intervals. Find sign of f(x) for x in each
interval.

Answer 1

a) f(x) = 0 <=> x = -1 or x = 2 or x = 3;
b) x∈(-oo, -1) => f(x) < 0;
x∈(-1, 2) => f(x) > 0;
x∈(2, 3) => f(x) < 0;
x∈(3, +oo) => f(x) > 0;