Determine the intervals on which f(x) is positive and on which f(x) is negative.

Question

f(x) = x^4+2x^3-13x^2-14x+24

f(x) < 0 if _____________________
f(x) > 0 if ____________________

Answer 1

f(x) = (x+4)(x+2)(x-1)(x-3)
f(x) changes sign where it crosses the x-axis.
Since f(x) has even degree, with a positive leading coefficient, you know that f is positive for x < -4, since all the factors are positive.
So, f(x) is
positive on (-∞,-4)
negative on (-4,-2)
positive on (-2,1)
negative on (1,3)
positive on (3,∞)