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+16x+16>0
What is the solution set?
(Type your answer in interval notation.)
shannon
Did it here, when you were MIKE
http://www.jiskha.com/display.cgi?id=1454677214
To solve the inequality x^3 + x^2 + 16x + 16 > 0, we first need to find the critical points of the polynomial. This can be done by setting the polynomial equal to zero and solving for x. However, in this case, there are no critical points as the polynomial does not factor nicely.
To find the solution set, we can use a graph. Here's how you can do it:
1. Start by graphing the polynomial function y = x^3 + x^2 + 16x + 16. You can use a graphing calculator or online graphing tool to simplify the process.
2. Look for the regions on the graph where y > 0. These are the regions where the polynomial is greater than zero.
3. In this case, you will notice that the polynomial is always positive. Therefore, the inequality x^3 + x^2 + 16x + 16 > 0 is true for all values of x.
4. Since the inequality is true for all real numbers, the solution set is the entire real number line. In interval notation, we express the entire real number line as (-∞, +∞).
Hence, the solution set of the polynomial inequality x^3 + x^2 + 16x + 16 > 0 is (-∞, +∞).