Question

Solve the polynomial inequality and graph the solution set on a real number line. Express the solution set in interval notation.
x^3+x^2+4x+4<0
The solution set is=

Answer 1

x^3+x^2+4x+4<0
(x^2(x+1) + 4(x+1) < 0
(x+1)(x^2+4) < 0

well, x^2 + 4 is always positive, so the only way the whole thing < 0 if
x+1 < 0

x < -1

check:
good ol' Wolfram webpage
http://www.wolframalpha.com/input/?i=plot+y+%3D+x%5E3%2Bx%5E2%2B4x%2B4

notice where the curve is below the x-axis ?

Answer 2

Thank you!!!