Solve the inequality writing it as an interval
Algebra

Tutor: None Selected  Time limit: 1 Day 
Solve the inequality
x^3 + 5x^2 >or equal to 4x + 20
Write your answer as an interval or union of intervals.
Please note that the sign is supposed to have a line under it making it 'or equal to.'
Thank you for the opportunity to help you with your question!
x^3 + 5x^2  4x  20 >=0
First, make this into an equation:
x^3 + 5x^2  4x  20 = 0
solve for x by factoring by grouping:
(x^3 + 5x^2)  (4x + 20) = 0
factor out common term
x^2(x+5)  4(x+5) = 0
Factor out the (x+5)
(x+5)(x^24) = 0
the x^24 is a difference of two squares and thus can be factored more
(x+5)(x+2)(x2) = 0
set each term to zero and solve for x
x+5 = 0 OR x+2 = 0 OR x2 = 0
x = 5 OR x = 2 OR x = 2
plot these on a number line:
______________________________________...
5 2 2
pick values in each interval to see if they satisfy the inequality:
10:
(10)^3 + 5(10)^2  4(10)  20 >=0
1000 + 500 + 40  20 >= 0 FALSE
1:
(1)^3 + 5(1)^2  4(1)  20 >=0
1 + 5 + 4  20 <=0 FALSE
0:
20 >=0 FALSE
3:
3^3 + 5(3)^2  4(3)  20 >= 0 TRUE
therefore are solutions is true when the value of x lies between 5 and 2 and when it is greater than or equal to 2
as interval notation:
[5, 2] U [2,inf)
Secure Information
Content will be erased after question is completed.