my professor doesn't lecture, instead we are given online "lectures" which never explained how to do this, and none of the reading went over the homework. I was ready to give up and flunk the homework, then I found this video and now I'm finishing the last problem. thank you so much for helping me, it took two hours to find this video but it was worth it. I am so happy.
This helped me so much. I probably have wasted more than 10 hours trying to figure this out with tutor help and I couldn't get it. Your explanation just makes sense and its to the point. Thank you!
I'm taking an online College Algebra class and her notes are never good enough for me to actually figure out what we are supposed to do. This was the only video I found that helped me. Thank you!
Thank you so much! You've cleared up a lot of confusion and made these equations look so simple when just a moment ago they seemed so complicated! It is amazing how a video made six years ago can still be so helpful to this day. ♡♡♡
My God! THANK YOU THANK YOU!!! I teach myself Pre-calculus since my teacher doesn't really teach this helped me out SO MUCH! You've taught me more in this vid then my teacher's 50 minute class :)
@Mayra Gonalez: The first two were in standard form, so the first term was the leading term. The third one was factored, and adding those exponents is what you would get if you multiplied all of the factors back together. This is called the leading term test, which determines how the ends of the polynomial graph behave. Please set you comments so that they can be replied to in the future, and let me know if you have more questions.
The third problem's degree: Understanding its degree took me longer than it should've. I kept thinking it should be a third degree equation, since three is the largest exponent. But then I processed it's all one term, not three terms added together, so each of those exponents has to get added to each other to get that single term's degree. Don't know if this'll help anyone since everyone seems to get it perfectly, but there ya go.
Thanks for the video...2 questions. When finding the multiplicity of g(x) (between 2min 35sec and 2 min 57sec) you say that the answer comes from the first factoring you did but I thought it was found from the original problem. Why is it done that way? 2nd Question..... The way you do it you say that (from right to left) that the 3 has a power of 1 but there is no x with a power of 1 there. You also do the mutliplicity of -4x and of x^2. But you point to the x^2 on the OUTSIDE of the parenthesis. What about the one INSIDE the ( )? Thanks! Heather
1st question: You are confusing the multiplicity of the factors with the degree of the polynomial. The multiplicity of all of your factors (1, 1, 2) should sum to the degree of the polynomial (4). The multiplicity of each factor determines how the graph will behave at those points. 2nd question: Pause at 2:59 --> I am saying that the power of X in the factor (x-1) is 1, the power of X in the factor (x-3) is 1, and the power of X in the factor (x^2) is 2. If this thing factored to (x - 2)(x-5)^2(x+3)^3 the multiplicity of these factors would be the exponents outside the parentheses. Does that make sense? Let me know.
How wil you know how high will the curve rise if there is no y-intercept for example there is only one y-intercept after hitting it how will you know how high the next curve will be if there is no y-int ?
+YAHOO These techniques give you a rough sketch. To determine the height of the hills/valleys would require calculus. There are usually two/three sections of a calculus 1 textbook solely devoted to finding local maxima/minima (the height and location of the hills and valleys). Hope this helps.
Wouldn't it work to simply plug in another few values for x? For instance if you knew you had zeroes at 3 and 4, then evaluate for x=3.5 to get a corresponding y value? I really appreciate that you answer questions here, that is so generous and awesome.
In regards to question #2, I noticed that the -2 that you factored out was not included in the fully factored final answer. Is there a reason for this? I'd appreciate a reply as I am a bit confused. I'm asking as I've decided to factor the polynomial by using the rational roots test. After synthetic division with a divisor of -3, I had a quotient of -6x^2+26x-24 with no remainder. I had factored out 2 out of this, leaving me with 2(-3x^2+13x-12). I factored this further, leaving me with 2(-3x+4)(x-3). So, with the first factor included in the fully factored answer, I have f(x)=2(-3x+4)(x-3)(x+3) Of course, this doesn't affect my sketch too much but I would like to fully understand the process.
h(x), g(x), etc are all function notation for y. Any multiplicity higher than 3 acts like a multiplicity of 3. Higher multiplicity will always flatten out at the zero, but it may go through the axis or it may turn and go back the way it came depending on whether the polynomial is even or odd.
A table of values is what you resort to when you don't have any other way of sketching a graph. For polynomials (where the zeros can mean a lot in higher math courses) you should always find the zeros and then sketch based on that. I hope that helps.
why does nobody explain how they are factoring their polynomials??? jesus Christ guys... this is like the 10th youtuber who cant seem to explain this stuff to me...
End behavior or zero behavior? End behavior is based on the Degree and the sign. Positive sign and Even degree both ends point up. Positive sign and odd degree - left end points down and right end points up. Negative sign and even degree - both ends point down. Negative sign and odd degree - left end points up and right end points down. I hope this helps. Let me know
my professor doesn't lecture, instead we are given online "lectures" which never explained how to do this, and none of the reading went over the homework. I was ready to give up and flunk the homework, then I found this video and now I'm finishing the last problem. thank you so much for helping me, it took two hours to find this video but it was worth it. I am so happy.
Thank you SOOOO MUCH. My professor can't explain anything worth a damn. You made it so easy. Thankyouthankyouthankyou!
Caitlyn Nicole c
This helped me so much. I probably have wasted more than 10 hours trying to figure this out with tutor help and I couldn't get it. Your explanation just makes sense and its to the point. Thank you!
I'm taking an online College Algebra class and her notes are never good enough for me to actually figure out what we are supposed to do. This was the only video I found that helped me. Thank you!
just wanted to say, this video hit the right buttons for me and got the sketching of polynomials through my thick skull.
thank you.
Thank you so much! You've cleared up a lot of confusion and made these equations look so simple when just a moment ago they seemed so complicated! It is amazing how a video made six years ago can still be so helpful to this day. ♡♡♡
I teach myself algebra and pre-calculus using youtube and I do very well. This was among the best videos I've seen, thank you so much!
You have no idea how much this has helped me!!
THANK YOU SO MUCH!!! The last example was exactly what I need!!
You are awesome!!! Keep the good work!
Your video really helped me out! The pace was perfect, your explanation was coherent, and I love your accent. Thanks so much!
I was confused about the graphing and the behavior; this v/d helped very much. Wonderful and thank you so much!!
Man your great!!!! Thank you best video I’ve found regarding this concept. Will be watching more.
Wow, the way you explain, is amazing! Thank you so much.
I am very glad I can help. This is the reason I make these videos. Good luck with your courses.
even after this long, this is still saving high school students everywhere.
I finally had my eureka moment that this type of problem finally made sense!!! Thank you so much!!!
My God! THANK YOU THANK YOU!!!
I teach myself Pre-calculus since my teacher doesn't really teach this helped me out SO MUCH!
You've taught me more in this vid then my teacher's 50 minute class :)
Thank you very much for sharing. This was incredibly helpful and I learned a great deal!
i just love your sound
and the way you teach too
@Mayra Gonalez: The first two were in standard form, so the first term was the leading term. The third one was factored, and adding those exponents is what you would get if you multiplied all of the factors back together. This is called the leading term test, which determines how the ends of the polynomial graph behave. Please set you comments so that they can be replied to in the future, and let me know if you have more questions.
I spent over 6 hours on class and Khan's academy and i still could noit get the damn end behavior.
THank you so much, it is so damn easy now!!!!
Thank you! The last example you did solved all of my problems.
Wow. With you is so easy. Thank you.
I was having trouble with this in my class and you just made it seem so much easier! Thanks you!
Thank you so much, I learned more in 15 minutes than I have in a month!
The third problem's degree: Understanding its degree took me longer than it should've. I kept thinking it should be a third degree equation, since three is the largest exponent. But then I processed it's all one term, not three terms added together, so each of those exponents has to get added to each other to get that single term's degree.
Don't know if this'll help anyone since everyone seems to get it perfectly, but there ya go.
Awesome video. Helped a lot. Is the easiest way to graph polynomials.
wow u are hero..thank you so much
Much thanks, explained in a way a lot easier to understand than how my teacher explained it.
Thank you so much, doing God’s work🙌🏾
Thanks a lot ! that was great !!! keep it up with the hard work.
thank you so much!! now i understand it so much better than before! :)
nice fountain pens, the lamy looks nice and i love my noodles. what is that green ink your using? btw thank you so much!!!
Noodlers Gruene Cactus.
+aggieneer02 thank you. It looked cool and stood out.
Keep up the good work!!!
Thanks, Exactly what i was looking for!
Super helpful! Thank you so much!
this is the best video ever!!! thank you so much!!
Thank you so much!! You made it a lot more easy to understand
This is amazing! So helpful.
it took me 10 minutes to solve 1 question before watching this. Now it takes me 2. Thanks!
Thanks for the video...2 questions. When finding the multiplicity of g(x) (between 2min 35sec and 2 min 57sec) you say that the answer comes from the first factoring you did but I thought it was found from the original problem. Why is it done that way?
2nd Question..... The way you do it you say that (from right to left) that the 3 has a power of 1 but there is no x with a power of 1 there. You also do the mutliplicity of -4x and of x^2. But you point to the x^2 on the OUTSIDE of the parenthesis. What about the one INSIDE the ( )?
Thanks!
Heather
1st question: You are confusing the multiplicity of the factors with the degree of the polynomial. The multiplicity of all of your factors (1, 1, 2) should sum to the degree of the polynomial (4). The multiplicity of each factor determines how the graph will behave at those points.
2nd question: Pause at 2:59 --> I am saying that the power of X in the factor (x-1) is 1, the power of X in the factor (x-3) is 1, and the power of X in the factor (x^2) is 2.
If this thing factored to (x - 2)(x-5)^2(x+3)^3 the multiplicity of these factors would be the exponents outside the parentheses. Does that make sense?
Let me know.
Thank u soo much sir for u r explanation
Great Video. Thank You!!!!!
you explained it perfectly thanks so much!!!
Awesome video! Thanks.
This helped me out so much! thanks
thanks for the video, as an Australian it was hard to adjust to the accent while learning but it was all good XD
omg thank you, you saved me
Thank you, you're awesome!
very helpful but what do you do when you cant factor out a number or a variable cause they all don't have x's or common dividers
very helpful. anyway, did anyone notice the phone ringing at the end of the video? I wonder if he answered it...
How wil you know how high will the curve rise if there is no y-intercept for example there is only one y-intercept after hitting it how will you know how high the next curve will be if there is no y-int ?
+YAHOO
These techniques give you a rough sketch. To determine the height of the hills/valleys would require calculus. There are usually two/three sections of a calculus 1 textbook solely devoted to finding local maxima/minima (the height and location of the hills and valleys). Hope this helps.
This helps. Thanks!
Wouldn't it work to simply plug in another few values for x? For instance if you knew you had zeroes at 3 and 4, then evaluate for x=3.5 to get a corresponding y value?
I really appreciate that you answer questions here, that is so generous and awesome.
THANK YOU SO MUCH the test is tomorrow and I didn't get this in class or on any other videos
Great video
can the ones from the x part be used in tandem with the possible roots of the full polynomial function?
Nice explanation. i have one concern graph of first question doesn't seems to be symmetric about y-axis. Can we ignore that fact while graphing?
Fantastic
Omg this helped so much! Thankyou!
Thank you sooooo much you just saved me from a zero
You’re my savior
thank u so much. It really helped me! :)
In regards to question #2, I noticed that the -2 that you factored out was not included in the fully factored final answer. Is there a reason for this? I'd appreciate a reply as I am a bit confused. I'm asking as I've decided to factor the polynomial by using the rational roots test. After synthetic division with a divisor of -3, I had a quotient of -6x^2+26x-24 with no remainder. I had factored out 2 out of this, leaving me with 2(-3x^2+13x-12). I factored this further, leaving me with 2(-3x+4)(x-3). So, with the first factor included in the fully factored answer, I have f(x)=2(-3x+4)(x-3)(x+3) Of course, this doesn't affect my sketch too much but I would like to fully understand the process.
Why did you add the exponents on the last problem to find the end behavior, but I'm the first and second one you just looked at the first coefficient
thanks so much!!
Hi beauti
I wish my brain went this smooth when doing homework
so if it is in factored form you have to add all the degrees and youll get if it is even or odd, right?
Thank you sooo muchh!!!!!! Now I can do my re-take!! :D
Thank you so much!!!!!
Great examples
Why in the 3rd example you added the exponents, but you didn't add the other examples?
His accent is so good
thank you so much this is really helpful :)
bruh you saved my soul
Nice pen!
@aggieneer02 Thank you so much, you make my head blow, positively I mean, because I realized how awesome math is :))
Life saver!!!!
This guy knows his shit
what is the difference of h(x) and f(x) are they both y ?
what about if i have multiplicity of 4 will it be a tangeant ?
h(x), g(x), etc are all function notation for y. Any multiplicity higher than 3 acts like a multiplicity of 3. Higher multiplicity will always flatten out at the zero, but it may go through the axis or it may turn and go back the way it came depending on whether the polynomial is even or odd.
aggieneer02 thanks man ..
Is this a calculus or precalculas topic? Bad question, but I am just trying to preview math before it really get underway for me this semester.
Algebra 2
Pre-calculus or college algebra. But it should be covered in HS Algebra 2.
Thank you so much!
What if it's negative but the exponent is an even number
I'm a bit confused. Our teacher taught us a technique using a table of values. What's the use of it instead of using the multiplicities?
A table of values is what you resort to when you don't have any other way of sketching a graph. For polynomials (where the zeros can mean a lot in higher math courses) you should always find the zeros and then sketch based on that. I hope that helps.
Okay. Thank you very much for the quick response. I really appreciate it
brilliant!
Nice video! Thx!
Thank you sir!
thank you !
well done
thanks so much!
thankyou sir
Thankyou
why does nobody explain how they are factoring their polynomials??? jesus Christ guys... this is like the 10th youtuber who cant seem to explain this stuff to me...
This is well beyond that. Check out videos on factoring. This is made with the assumption that you know how to factor well.
great explanation
anybody know which lamy pen that is?
Thanks
How do we know the behavior
End behavior or zero behavior? End behavior is based on the Degree and the sign. Positive sign and Even degree both ends point up. Positive sign and odd degree - left end points down and right end points up. Negative sign and even degree - both ends point down. Negative sign and odd degree - left end points up and right end points down.
I hope this helps. Let me know
@@aggieneer02 infinity....tha ks though
Love you
thx
Bounce lol
lol
thank you
THAT ACCENT THOUGH!!!!!!!!!!!!!!