Answer to polynomial inequality in interval notation?

[jhoffy22]

I need to solve this polynomial inequality. (x-3)(x+2)(1-x) is greater than or equal to 0. I need to put the answer into interval notation but I'm not sure how too. I have been struggling with this for quite some time. Thanks in advance for the help!

So far, I know that:
(x=3), (x=2), and (x=1) are the x intercepts.

I put all these on a number line and then test values from interval and know to pick the intervals that satisfy the inequality but I don't know how to write it. Please help me.

 

[tkhunny]

You have:

x = -2
x = 1
x = 3

For these three values, the value is zero. With three breaks, you have four intervals.

I'm a little troubled that you can pick values from intervals but cannot name the interval.

\(\displaystyle (-\infty,-2)\;\;(-2,1)\;\;(1,3)\;\;(3,\infty)\)

 

[jhoffy22]

I don't know how to put them in union with each other, but thanks for your help.

 

[mmm4444bot]

I don't know how to put them in union with each other

Then you could have asked instead, "How do I write the union of two intervals?"

If you want specific responses, you need to ask the right questions.

Use the union symbol \(\displaystyle \cup\) (from set notation), to write the union of two or more sets.


EG: Write the union of the sets (-4, 7) and [15, 20]

\(\displaystyle (-4, 7) \cup [15, 20]\)

Please share your results, so far, if you would like more help with this exercise.

 

[tkhunny]

"or" of course.