Exponent Rules & Polynomials

[@kiteoootim7552]

1 month full of boring ass classes, homework, class work, and lectures.... While this dude just explained the whole damn unit better than the teachers in 10 minutes.... This is why I hate school.

[@hassanhashemi9933]

Kite AnimeVids ikr

[@emilylast839]

O my gosh!! That is so true 🙄🙄

[@carolinepacifico9982]

yea literally, i just depend on youtube now to teach me math bc my teacher f sucks at teaching

[@somewhatcrazy9461]

I know this vid was made wayyyy back in 2011, but when I found this, I was actually learning something. This helped me in my math class and I'm about to take the test in a few days. Thanks George! :)

[@alextuzz1751]

Every teacher needs to be like you

[@daniaihsan1830]

alex tuzz Za

[@pattyjoseph8470]

For Problem 9, I had the exact format but with an exponent outside the parentheses like in Problem 12. And for the life of me, I could not figure out the answer until I stumbled upon your explanation for Problem 12. I applied your steps and got the right answer after more than half an hour of trying different ways to solve it and watching so many KZbin videos. Thank you so much for relieving my headache.

[@kevinjames9724]

Your direct and concise approach to each challenge is what every math teacher should aspire to. I'm now a subscriber of your videos and look forward to any future ones you decide to make in regards to math. Gratitude!

[@ashleyford4464]

I have a test in algebra later today and I've really been struggling. I think watching this before going into the test is really going to help boost my grade! Thank you so much!

[@georgewoodbury]

+Ashley Lester Let me know how you do. Good luck!

[@Sugarfairy89]

Ashley Lester heh she never told you

[@user-el6lt8fr3x]

Sarah Yoongi hehe yeah it’s been 2 years

[@crayoncookie9047]

Amazing! Going back to college after years and having to retake the placement test has me in panic mode. Thank you George for making this a great lesson and reminder for me without setting me back hours!

[@georgewoodbury]

I think the best move is to take log base 5 on both sides. That will give you x-4 = log (base 5) of 3^(2x). Use exponent property: x-4 = 2x log (base 5) of 3. Collect terms containing x on the left side, constants on the right side: x - 2x log (base 5) of 3 = 4 Factor out x: x [ 1 - 2 log (base 5) of 3] = 4 Finish by dividing: x = 4 / [ 1 - 2 log (base 5) of 3] By the way, log (base 5) of 3 can be rewritten as ln(3)/ln(5). With a calculator, the solution is approximately -10.95.

[@themaggattack]

Praise be to KZbin and praise be to Mr. Woodbury. I have been delivered from failure. Hallelujah! (That's just my dramatic way of saying thank you so much, this was reeaaalllly helpful!)

[@georgewoodbury]

themaggattack Hahaha - you made my day! Glad it helped.

[@themaggattack]

George Woodbury... Good, I'm glad, bc you made mine, too! 😁

[@hellojuneau8917]

Used this to review for math proficiency exam. Thank you!

[@georgewoodbury]

You are welcome - good luck on your exam!

[@dylancarpio317]

I have the worst math teacher ever and it’s making my grade 9 math grade so low, thank you so much for explaining this so easily. I don’t usually comment but you deserve the good feedback 🙌

[@georgewoodbury]

dkcarpio _ Hang in there - you can do it!

[@manuelvillalpando6665]

Thank you for this informative video. I think that most Math teachers are so focused on quantity vs. quality that they don't teach the fundamentals to the point where the RULES are thoroughly understood. Instead, most teachers focus on assigning more work, when in fact a student needs more training on the fundamentals. I really like this video because if emphasizes a bit more on the Rules. Thank Mr. Woodbury for the video.

[@DeDeDossier]

This helped me so much, you explained this better than my teacher ever did. Instead of a bunch of worksheets I got this all down in 3-4 notebook sheets of paper. Thanks

[@ninaradley5229]

Thank you! I needed to review the rules of exponents for taking the accuplacer. This was incredibly helpful and it alerted me to several mistakes I've been making.

[@crikenfan223]

you just helped a student out in 2021. Thank you! extremely helpful and easy to understand

[@TheConvicted0nes]

Its about time... This well made video answered questions that were skipped in other video's. Thank you!

[@stephanierobb3270]

This video was made back in 2011 and in 2020 its still helping people. Good job George! You really helped me here! A+!

[@jennidarqnys93]

Thank you. This explained in less than 20 minutes what pouring over Pearson's algebra took me hours and hours and I was still confused! I have a test on this on Monday and thanks to you I know I will pass now!

[@WatchAngelTV]

THANK YOU THANK YOU THANK YOU!!! I am sooooooo happy I found a video that cover EVERY aspect of working with polynomials.

[@musicfriend2051]

Hi it’s 2019. Thank you.

[@madisonsmith4821]

Hi it's 2020. Thank you.

[@Shin-hj4mc]

hi its 2021 thank you

[@JSVR4021]

Thanks! This clarifies alot! Please don't stop making videos like this!!

[@georgewoodbury]

Thanks Jenna!

[@georgewoodbury]

Hi Carlos - You can only use your method when there is one term in the parentheses. If you are squaring a binomial with two terms, the first step is to rewrite the problem as a product. In this example it becomes (7x-2)(7x-2). Then multiply, using what most call "FOIL". If the problem was just (7x)^2, then you can square each factor to get 49x^2.

[@vadaphillips4853]

Preparing to go back to school and luckily I found this video. Thank you! This was so helpful.

[@tatumross2699]

thank you sooooo much!!! this helped my study for my math test that i was sooo scared for and you made me understand everything in 16 minutes!

[@georgewoodbury]

Glad I could help!

[@transimica]

You are great!!! Thank you for taking the time to do this video. It was very helpful...

[@georgewoodbury]

Good question - here's a couple of reasons. 1. Think about what 7x times x would be. 7x times x is 7x^2. 7x times 7x would not give you the same answer as 7x times x. 2. We can use the commutative property to rewrite 7x times 7x as 7 times 7 times x times x, reordering the factors. We know that 7 times 7 is 49, so 7x times 7x equals 49x^2. Does that help?

[@georgewoodbury]

@A0Candle0In0The0Dark The rules in this video don't apply to a sum like x+h. You have two options. 1) Multiply (x+h)(x+h). Then multiply that answer by (x+h). Then multiply that answer by (x+h). Then multiply that answer by (x+h) until you have (x+h)^5. 2) Search for the binomial theorem, which is a short cut for raisinh binomials to a power.

[@dnbmonkey83]

Thank you! This was the perfect find for my test I have tomorrow :D You covered everything in our chapter. THANK YOU SO MUCH! Maybe this time I won't fail.

[@sasaeteurn]

I was wondering if you have any videos on rate and probabilty questions?

[@fuzzykropolis]

Thank you so much. I found this very helpful for my Algebra I class. Gonna recommend it to my classmates. I haven't done any of this stuff in years & was really worried about my test coming up.

[@sinfulcolor10]

Great explanations Mr. Woodbury thanks !!! Much easier to understand along with the book Elementary Algebra custom edition for PCC

[@sasaeteurn]

Thanks George. This was so helpful. You are awsome!!! You make things a lot easier to understand. Again, thanks for all that you do.

[@georgewoodbury]

One other thing to consider - what is 7x times 6x? 7 times 6 is 42, so you have 42x^2. That would imply that 7x times 7x is 49x^2. Now it would be true that 7x times 7x is (7x)^2, but that still will simplify to be 49x^2.

[@JoeCnNd]

3:20, glad you brought this up. I wasn't sure if the -5 went down or not.

[@brookesearcy6445]

ughh ty!! the perfect vid to help me study for my algebra quiz

[@georgewoodbury]

I hope you do well on your quiz.

[@nicobello4226]

8:32 the answer is actually wrong...why 6? it is supposed to be 28.

[@georgewoodbury]

Nico Bello - When we have -17 - (-11), that is the same as -17 + 11 which ends up being -6.

[@mstephens7299]

Thank you! I am studying to take the College Algebra CLEP and I think watching your videos will be such a valuable resource!

[@georgewoodbury]

Good luck with your exam, Margaret. Let me know if you have any questions.

[@felsicboi9945]

Hey, you're not alone. I'm taking my exam tomorrow.

[@leo82027707]

thanks so much, I am taking an intro to algebra lass and it's been really hard to grasp the concepts!!!!!! So easy to understand!!!!!!!

[@georgewoodbury]

You are welcome! If you have any other topics of interest, swing by my web site and submit a request - the address is at the end of this video.

[@barrettgilbreath7500]

This guy just thought me more in 16 minutes than my teacher thought me in 2 weeks!!!

[@georgewoodbury]

There are two ways to go with this one. 1) Multiply (2x^3 + 3y^2)(2x^3 + 3y^2) using "FOIL". Then multiply your answer by (2x^3 + 3y^2). That way you will use (2x^3 + 3y^2) as a factor 3 times. 2) You could use the binomial theorem. I don't have a video for that approach, but it should be easy to find through a search.

[@georgewoodbury]

@ebblondie You're welcome - that's great news! Polynomial division can seem so complicated at first, but once you get the pattern it's not so bad. Keep up the good work.

[@Anna-zt8he]

I have a test in a day from tommorow and I appreciate this

[@jaydengelvin6955]

2020 and this is a life saver. thank you sm george

[@georgewoodbury]

Thank you. If (x-4) is the exponent for 5, then that equation can only be solved using logarithms. Have you covered logarithms before?

[@georgewoodbury]

@sasaeteurn You bet! Let me know if there are any topics I can help you with.

[@marthamahe5898]

I don't get what the answer was at 13:23 Was it 3x+3 -9/24?? And should you always do long division when trying to divide polynomials? Thanks for the help though. Helped A LOT.

[@georgewoodbury]

martha mahe Hi - the denominator of the remainder is always the divisor, which is the x-4 from the original denominator. Later in the course you can try reducing the fraction instead of dividing if the numerator and denominator can be factored. At this point, though, if the directions say to divide you should use long division.

[@mbot48]

This is alright needs more explanation on the rules applied tho. For the problem -5x^6y^-4z^-7 WHY? do you move the y^-4z-7 down into a fraction/quotient please explain?

[@jillybeanz147]

@ around 10:00 he says 5x • 3x is 15x^2 and I don’t understand why it would be squared

[@joshuamartin1999]

Thank you sir! This summed up everything better than 2 weeks of class!

[@georgewoodbury]

Glad to hear that - good luck in your class!

[@thisisblackmesa]

Thank you so much!

[@georgewoodbury]

I'm happy to help!

[@CrypticDream5]

Good video, really liked the variety of problems

[@lemyaknight]

Thank you for this video, I understand this better to help my students...Keep them coming!

[@alexdelgado7367]

I actually live in Tulare I was getting ready for the Tulare county math Superbowl I hope I do well

[@vampireghouls]

OH THANK YOU I NEED THIS FOR MY TEST TOMORROW! Tysm LIFESAVER 😆

[@gladystyo3565]

Thanks, it helps me a lot for Algebra test tomorrow :)

[@Jasmin-bp6ic]

I really needed this, hopefully I don’t fail my test tomorrow!

[@americanstates4331]

HAHA, This is GREAT!!!! THANK YOU!!! I GET IT!! WOW! Been struggling til now. You are awesome!!

[@TheConvicted0nes]

Im going to watch this video 100x so i stop forgetting exponent rules LOL

[@TheHaloop]

Thank you so much! I couldnt find any other good videos.

[@donathan2933]

so the exponents can go beyond 3?

[@OliveandWreath]

This really helped me out a lot. I really like your video explaining all steps

[@georgewoodbury]

I'm glad to help!

[@judojustim]

aah ok yes that does help. thank you for the speedy response

[@brandonfarrar3475]

This will help for my North Shore Community College placement test. Thank you so much.

[@kellyportillo1361]

Brandon Farrar me too!!

[@kekethomas1586]

Mr. George my son is in Algebra and because hw had to miss school,he fell behind. He returned to class and came home with polynomial problems to work that he does not understand because he misses the instructions and rules on how to do them. Can you possibly show us how to solve this problem. (a^2b^4c)^-2 × (ab^2c^2)?

[@georgewoodbury]

Sure. The first step is to raise each factor in the first set of parentheses to the -2 power, by multiplying each exponent by -2. (a^-4 b^-8 c^-2) x (ab^2c^2) Next simplify each base (a,b,&c) by adding their exponents. a^-3 b^-6 c^0 Any nonzero base raised to the 0 power is equal to 1, so you can ignore the c. a^-3 b^-6 Now you should rewrite the answer without negative exponents. Since both bases have negative exponents, they get moved to the denominator, leaving the number 1 in the numerator. The exponents become positive at that point. 1 ----- a^3 b^6

[@sbaby-fc3ki]

Excellent instruction!!!

[@randomofasound]

Can you please show more division polynomials. In short detail! I got so confused at the end!

[@georgewoodbury]

Hi - I will see if I can put together a couple more soon. In the meantime, there is one more at the end of this video: kzbin.info/www/bejne/gJCYqGl7eLOVhpIm22s

[@randomofasound]

Thanks! It's just the steps for me I do not get until they are broke down in detail steps :[!

[@miyabrown8382]

I thought that when you subtract polynomials you suppose to change the minus sign to an addition sign

[@judojustim]

on problem 12 why wouldnt 7x times 7x be 7x^2 ?

[@MAP0491]

I should pay you to teach me instead of my teacher. Im in college and i hate math. But after every class, i have to come to this page to actually LEARN what was supposed to be taught in class today. my teacher sucks at teaching. So, thanks!

[@starponys0740]

What really makes polynomials seem familiar is this revelation: that they are simply the general form of the place-value system. I have a video on my channel that will hopefully open the concept even to third graders. (It is titled "Place Values: The Window to Advanced Math.)

[@Roxas1s]

So much better then my Math Teacher!!!

[@AlejandraRodriguez-rn1zp]

really liked it very helpful thx!! exponent part very useful...

[@ericchhun8116]

so, you said if it's a number it doesn't move. even if it was a -5^-6 it still doesn't move right

[@georgewoodbury]

If the exponent is negative then the base moves whether it's a number or variable. -5^-6 = -1/5^6 = -1/15625 (-5)^-6 = 1/(-5)^6 = 1/15625

[@raymondklawson382]

You helped me alone with this video. That's great

[@cessdeguzman]

Im having a quiz about this tomorrow and thank you very much bc ur video really helps :)

[@Thegooob95]

@georgewoodbury you sir are a God! thank you!

[@jennifertorres6325]

Thank you George, you saved me today!!

[@dcelo1072]

at 11:22 is it a positive 28 lol?

[@georgewoodbury]

No, when combining two like terms that are negative you add the numbers but the total stays negative.

[@xokizza]

nicely done great review for my test on tuesday!! =)

[@Jurniie]

Thanks haha you helped me study my Algebra final! Im trying to Ace it c; Hopefully I got everything down. Cause now Im totally getting it.

[@genesisbalbuena9090]

Thanks!! This helped soo much

[@georgewoodbury]

You are welcome Genesis. Best of luck!

[@FranciscoSanchez-mp5tz]

really cool video!

[@georgewoodbury]

Thanks Francisco!

[@dnbmonkey83]

I swear I learn more from youtube math videos too.

[@dagoat9715]

thx this helped for my Benchmark! Your the best Bro!

[@TheSkatersk8terskate]

this is fantastic thank you so much

[@brandonworrall185]

Like do the box method if you know that and more binomial and polynomial problems...but thanks for the help it was very helpful

[@georgewoodbury]

+Brandon Worrall I do have another video with a few more of these types, but no box method. Check them out here: kzbin.info/www/bejne/gJCYqGl7eLOVhpI I will put together some more shortly.

[@brandonworrall185]

I don't understand some other kinds of problems that are just like this but you didn't do them....can you make another video with similar but different problems

[@georgewoodbury]

+Brandon Worrall If you can give me an idea about the type of problems I can definitely put something together.

[@coltonmarwill475]

this video was very helpful, thanks!

[@georgewoodbury]

Colton Marwill Glad to help out!

[@mingogirl2012]

I have bonus work that's due tomorrow. The question is (2x^3+3y^2)^3 HELP PLEASE!

[@the_david_hayes]

best exponent review ever

[@calciferardor8791]

I don't get it .__. (typical grade 8 on summer holidays)

[@elladonaire7139]

Thank you, this video helps me a lot.

[@georgewoodbury]

Excellent! Good luck!

[@jeanetteromero3272]

I love math!! it was awesome!!!

[@georgewoodbury]

@Shukria123 Thanks!

[@veniceplayss8275]

This helped a lot thank you

[@williamromero9989]

Great video! This guy right vvvvvv

[@hassanhashemi9933]

thank you sooo much sir

[@chrissystewart6268]

It look easy to me I'm glad I learning algebra I hope I passed My G.E.D

[@chrissystewart6268]

I never learned this in school my goal is to be great in Algebra I hope I passed my GED