Solving Polynomial Inequalities

This precalculus video provides a basic introduction into solving polynomial inequalities using a sign chart on a number line and expressing the solution as an inequality using interval notation.
Introduction to Polynomials: • Polynomials - Classify...
Polynomials - Basic Operations:
• Polynomials - Adding, ...
Dividing Polynomials By Monomials:
• Dividing Polynomials B...
How To Graph Polynomial Functions:
• How To Graph Polynomia...
Intermediate Value Theorem:
• Intermediate Value The...
_____________________________________
Long Division - Polynomials:
• Long Division With Pol...
Polynomial Long Division - More Examples:
• Polynomials - Long Di...
Synthetic Division of Polynomials:
• Synthetic Division of ...
Remainder Theorem & Synthetic Division:
• Remainder Theorem and ...
Factor Theorem & Synthetic Division:
• Factor Theorem and Syn...
Rational Zero Theorem:
• Finding All Zeros of a...
______________________________________
Real & Imaginary Solutions - Polynomials:
• How To Find The Real &...
Solving Polynomial Equations - Synthetic D:
• Solving Polynomial Equ...
Solving Polynomial Equations With Excel:
• Solving Polynomial Equ...
Writing Polynomial Functions Given Zeros:
• Writing Polynomial Fun...
Descartes Rule of Signs:
• Descartes Rule of Signs
Solving Polynomial Inequalities:
• Solving Polynomial Ine...
_____________________________________
Final Exams and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
/ collections

[@TheOrganicChemistryTutor]

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[@plutoqueen7295]

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[@jlobz_8128]

tip: you don't need to solve all 3 regions, just solve the one on the left. once you solve it, then the region to the right will always be the opposite sign of what the first one is and so on

[@kiwistuffypistachio2558]

I’m gonna comment on this so I can remember

[@mistadude]

You can also solve the one on the middle or the right too the right might be easiest

[@reallybad7062]

Another tip: sometimes inequality can have more than 3 sections. Just make sure you solved all your roots, then you can assume.

[@sirdele]

i always check 0 and then one of the regions checks out

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Can you prove it? Generally. Not with examples! 🙂

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[@georgesadler7830]

MR. Organic Chemistry Tutor, thank you for a fantastic video/lecture on Solving Polynomial Inequalities in precalculus. These are strong analytical tools for all levels of science and engineering.

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ive been trying to do these for 2 weeks, 2 videos anf boom ik it all

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[@kirbyjames5837]

Our exam will be conducted tomorrow and im struggling in solving polynomial inequalities but look what I have found. Thank you for this video. It really helps me a lot.💖💖💖💖

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Thanks for saving my interest in calculus like inequality , domain....

[@f.a3202]

is this done in calculus in college? I'm in high school and I'm doing theese. now i feel a little more confident

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@@f.a3202 not really

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Thank you I understand your explanation 100x better than my teacher. Probably because she tried her own video instead of giving us a video.

[@castlerock7423]

Ok, I have a question. Instead of using the Rational Zeroes Theorem and then moving to Synthetic division, why didn't you just use Synthetic division to begin with as it gave you the remaining factors of the Quadratic? Wouldn't it be easier to do it that way? Also, I just wanted to say thank you for being here. You're wonderful.

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[@saveoursquirrels4241]

In factoring by grouping, what if the groups we're left with aren't the same? I ended up with x^2(x+10) - 1(11x+180) from x^3 + 10x^2 - 11x - 180

[@robvinsky]

I didn't even need to watch the whole video to have a better understanding of this topic than what Aleks could provide

[@aurumon]

Hello, @ 3:33, why is the answer "or" and not "and"? Doesn't the union sign in the interval notation mean "and"? Thank you.

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[@justinsantos5751]

After finding the points where y is 0, I graph it and it is much faster. You just have to be familiar with the graphs and plot the points where y is equals to 0 only. Works better for me.

[@lindo5100]

I do the same

[@Pianomantodd1]

What happens if your factors are the same (and are less than zero) and it's NOT also "equal to zero" (in a "less than" situation, or vice versa)? (x-3)(x-3)

[@castlerock7423]

She didn't specify the use of the term "test numbers" which are the numbers inside each interval that was created using the zeroes (or whatever number amounts to the inequality equaling zero. In this case, the zero would be 3, and the interval notation would have to be (-infinity, 3) because if you take one factor of the above you have x-3

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[@joeleapen8298]

For the last problem, isn't it x=-1 instead of x=1, because when you do synthetic division you're putting the "h" from "x-h" on the upper left corner, so in this case where we have 1 as our "h", wouldn't it be "x-1" and to solve for that value of "x" we had we just set "x-1" to 0 and solve from there, so it would turn out to be "x-1=0" which turns to "x=1".

[@DarkMatterr]

You assumed -h is being used in synthetic division accidentally. x-1=0 so we use 1 in synthetic division. Same goes for finding the roots since the root is the number being used in synthetic division if it's not an imaginary number.

[@mercier300]

Thank you so much! My teacher did such a horrible job explaining this! But you were fantastic

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9:50 How did u divide like that??? I only now long division help pls.....

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[@ronvelosangeles]

At 6:09, are you using the zero product property to get those answers?

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[@acv976]

For the problem at 8:45, couldn't you use the grouping method

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What is the rational zero theorem?

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[@adityapantula4850]

Your lectures are top of the class no offense. But wouldn't it be easier if we apply the wavy curve concept rather than calculating what will be positive and what will be negative and then determining the range of X....... Just a suggestion though

[@Jamaimer]

on the third problem, at the end I got + - + + instead of that you got which was - + - +, did i add wrong somehow?

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So whats the point on solving the regions?

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x - 3 > 2, x > 5

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can someone tell me why the sign doesn't change when the multiplicity is even? pls 11:40

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