O Hawkes L earning C Chegg Study I Guided solution x C https

O Hawkes L earning C Chegg Study I Guided solution x C https://learn hawkeslearning.com/ Portal/Lesson/lesson certify Save & End Certify Lesson: Chapter 4 Review 18/31 Question 14 of 20, Step 2 of 2 Correct Consider the following polynomial inequality. x (x+ 4)(x-5) 0 Step 2 of 2 Test each interval to find which ones satisfy the inequality. Express your answer in interval notation. Answer SHELBY Keypad Hide Submit Answer

Solution

x²(x+4)(x-5)>0

First we have to find the critical points and to find it we have to set the given expression to zero

x²(x+4)(x-5)=0

x=0,-4,5

So the regions to test are (-infinity,-4),(-4,0),(0,5),(5,infinity)
In first region,we get a positive term, so that region is a part of the solution set

In second region,we will get a negative term,so this region is not a part of the solution set

In third regionwe will get a negative term,so that\'s not a part of the solution

In fourth regionwe get a positive term,so that\'s part of the solution set.

Hence the answer is

(- infinity,-4)U(5,infinity)