Solve the polynomial inequality and graph the solution set on a real number line. Express the solution set in interval notation

Question

x^3+x^2+16x+16>0
What is the solution set?
(Type your answer in interval notation.)

Mike

Answer 1

use grouping to factor ...
x^3 + x^2 + 16x + 16 > 0
x^2(x+1) + 16(x+1) > 0
(x+1)(x^2 + 16) > 0

only one critical value , x = -1

so y = x^3 + x^2 + 16x + 16
is a cubic which is above the x-axis for all values of x, such that x > -1

I will let you write that in interval notation