Pre Calculus: Solve the following inequalities using interval notation

Question

f(x)= 5x³-4x²-7x+5 and g(x)= -x⁴+4

1. For what x-values is f(x) > g(x)
2. For what x-values is f(x) < 0

Answer 1

5x^3-4x^2-7x+5>-x^4+4

x^4 +5x^3 -4x^2 -7x +1 >0

x=-5.59, -1, .134, 1.356 are the interval boundaries, the x-intercepts, the roots

2 negative, 2 positive

(-infinity,-5.59)U(-1, .134)U(1.357,infinity)

use a graphing calculator, online or handheld such as TI-83