Let’s Factor This Polynomial … Step-By-Step…

[@t.birmingham2668]

I am 67 years old and really enjoy going over these problems. Thank you for your videos.

[@silverwoodchuck47]

Since the coefficient of the quadratic term is 1, just think of two numbers that when added sum to -4 and multiplied have a product of -21. Obviously the numbers are -7 and +3 because -7 + 3 = -4 and -7 * 3 = -21. So (x - 7)(x + 3). QED.

[@mdstarr1]

his video is over 14 minutes, the answer takes no more than 5 seconds !!!!!!!

[@ljcl1859]

@@mdstarr1 Because he is trying to explain it to people that still don't understand.

[@vanessahansen3644]

You explained this way better than my teacher thank you!!!

[@chrystelleheldire581]

Used to love maths. Lost it all apart from your everyday arithmetic. So sight to return and be excited about maths again. Thank you so much.

[@b213videoz]

I used to hate it... or rather it used to hate me 😂😊

[@maryahmed4899]

Me too ! Now I can’t wait to share with my 8 yr old …

[@ellchurch7314]

Just say, “find 2 numbers that multiply to give you -21 and add to give you -4”. Done

[@GenX4ever]

Sometimes one needs to see the steps to start to understand. I did. My brain just works like that. I always wished it was as easy as it was for some people.

[@ellchurch7314]

@@GenX4ever hi Justin I totally get the need to understand the concept. Factoring a trinomial is basically doing “foil” in reverse. If you FOIL (x-7)(x+3) you will see how the numbers work. You get X^2 + 3x-7x-21. Notice the 2 numbers in the middle. They will add to give you -4, and the same 2 numbers will multiply to give you -21. So when you add everything together you get x^2-4x-21. So let’s factor X^2-4x-21 (2 numbers that multiply to give -21 and add to give-4 are, -7 and +3. Replace the middle number with-7 and +3. Order doesn’t matter.) X^2+3x-7x-21 (then put in some brackets) (X^2+3x)(-7x-21) (in the first set of brackets factor out an x)(in the second set of brackets factor out-7, and see what happens) X(x+3)-7(x+3) (now we factor out (x+3) in math world, but keeping the math language simple just think about this. Notice that we have 2--(x-3)s, write it down once.then combine the x and -7 for the second factor) (X-7)(x+3) Hope this helps with your understanding. For factoring, it makes it incredibly more easy if you know your multiplication tables. So check my comment again and see if it makes a difference. Justin just an fyi, I have a science degree and an education degree and I’ve been teaching math for over 30 years and I just found the video a little long winded, and kind of all over the place a little. Good video if it works for you, but not how I would teach it. If you do have any other math questions, feel free to ask. All the best..

[@GenX4ever]

@@ellchurch7314 Thanks for the explanation. I've just begun looking at math again after 25 years of ignoring it. Fortunately I'm a hairdresser and salon owner so other than basic math that's all I've needed. I truly detested it for many years because it's the only subject in school I failed miserably and caused me to drop out of college from pursuing an art degree to teach art. Anyhow now I'm giving it another look and maybe different approach. Cheers

[@ellchurch7314]

@@GenX4ever Hi Justin Trust me, your view of math is a view shared by many. I have heard phrases like, “I hate math” or “when am I ever going to use this stuff” so many times it still makes me cringe. But honestly nobody likes things that they are not good at. I hate skateboarding because I suck at it. I keep falling off, so I quit trying. Maybe if I kept trying I wouldn’t fall of anymore and eventually even like it. Same thing with math. Failing at math time and time again is very frustrating but every Pro skateboarder gets back on that board. I think that it’s quite admirable that you are taking another crack at math after all these years. Good for you! If you have any questions, just reach out. I’ll be happy to help you.

[@brothercaleb]

😂

[@mendozajovy]

I get the factors of -21. 7 and 3 are its factor. Then determine which 7 and 3, negative or positive, to have a -4 middle term. (X-7)(x+3)=x^2-4x-7

[@kenwood4799]

OMG. Please just get to the point and quit the rambling. You are exemplifying why kids hate learning math from some teachers. Need a "speed it up" button. You took what should have taken about 2 minutes and drew it out for 14+ minutes. Oh, and thanks for the C2 description - which you never got around to explaining.

[@jimothygoldfish]

There is a speed it up button. It's called Playback speed, put it to 2x and stop crying lol

[@dennisoyston]

@@jimothygoldfish Another answer to that is to put the marker to the end of the red line! Just a few seconds left.

[@lamper2]

He actually took the time to explain WHY he does what you ignorantly call " rambling" watch it again when you aren't as arrogant

[@vlsui66]

@@jimothygoldfish that's not how it works. This teacher takes way too long to answer one simple question

[@vlsui66]

@@lamper2 he should do that "why" part in another video, not this. Some viewers already know the method, they just become stuck and come to this video for a quick explanation, not to reteach everything again. The title of this video isn't "How to factorise quadratics", it's "factorising x2-4x-21". He should stick to just answering rather than giving the whole background and content around it.

[@Sandyquinones11040]

Skip to 2:22

[@decentkaonde112]

This is lovely. I do not mind the time taken. I got the concept. Thank you.

[@moodiblues2]

Math was never my strongest suit, but I successfully got thru it up thru trig in high school and college. My graduate degree, Juris Doctorate, didn’t have any math as a requirement. But I’m not totally math illiterate. But this was the most confusing convoluted math video I’ve seen.

[@unicornfrenchbulldogs1063]

Exactly, same for me. I got lost when you began adding the common factors on the right.

[@devonwilson5776]

Quite informative. Factoring is very easy for me be it those containing x to the second power or those containing X to the third power. Usually, I do the factoring by inspection. Your method is great but rather lengthy.

[@henkhu100]

and the method only works in very special cases. Try x^2+18x-4200 Still a "great" method?

[@bradlewis8036]

Attention Elliot Churchill, just some food for thought on your comment. Instead, John is showing the complete solution and a full explanation so that people looking to learn or be refreshed cannot possibly be left to just automatically have to know everything. Therefore he does what any more knowledgeable person would do when he doesn’t know the education of every possible viewer. John is simply ensuring there cannot be any body that doesn’t learn anything because he just assumed all know a certain bit about the problem. I fully respect and appreciate your videos John because I had an injury that has affected a descent amount of my knowledge. Therefore I am enjoying your videos very much. I just need to buy a notebook before I purchase your courses. But I have relearned so much from your videos which has pushed me to use Google to find other math problems and courses to keep practicing math that will have me fit for my jobs when I get back to em. Thank you John for the videos. And I’m anticipating purchasing most, if not all of your courses.

[@dragondora654]

U r video is mindblowing

[@tamra9396]

I'm from the 80's and still prefer procedure. Thank you so much.

[@keppela1]

Linguistically, I don't think a monomial can be considered a polynomial as mono refers to "one" and poly refers to "many" - i.e. mutually exclusive terms. I'd be interested to know if there's an exception for math.

[@Peakosprey]

Polynomials are terms for equation with 4 or more, lower you have trinomial, binomial, and monomial

[@keppela1]

Well, since poly means "many", I can see how something like a trinomial might be considered a polynomial, but not a monomial.

[@SeattlePioneer]

I was able to factor this just by looking at it. It was obvious that multiplying the second terms had to produce a result of -21 and that adding the second terms had to produce -4. (x-7) (x+3) was thus easy to determine for a result.

[@moshemoses7105]

I love step by step prosidure you are best teacher ever

[@sumateeracha1280]

Good teaching

[@vrendus522]

Great thanks

[@johnplong3644]

Interesting way to do this problem I was never not taught that way

[@sariahgeorgiapeach1287]

thank you! it was very nice the way how you explained this!😁😁

[@GySgt_USMC_Ret.]

11:16 Ad pops up showing a man flipping a steak on a grill when the instructor says "and you're done". Happy New Year! Fair winds and following seas to all.

[@patriciagreen2365]

Great review of factoring trinomials.

[@pasavant]

Clear explanation, but why is factoring so important? What is factoring used for?

[@vlsui66]

Its used for solving equations. If you put x2-4x-21 equal to 0, then you can factorise and solve to find x. An example of a problem might be, there's a rectangle with length x and width x-4. The area of that rectangle is 21cm2. So what you would do is A=l×w, then 21=x(x-4), then 21 = x2-4x. Then you would bring 21 to the other side. x2-4x-21=0. Then you would factorise to get (x-7)(x+3)=0. The value of x would be 7 or -3. -3 isn't correct because it is negative, so x=7cm. The length is 7cm and the width is 7-4=3cm. To check, 7×3=21cm2. Boom. That's one example of factorising being useful.

[@mwenpapdiw7700]

You’re making a simple factorization into a mumbo jumbo! In my head (X+3)(X-7).

[@vlsui66]

Correct. This teacher takes too long to answer one simple quadratic.

[@robpatterson2861]

You are an awesome teacher! I enjoy these videos very much. Thankyou!

[@v-gc7257]

Very helpful

[@beehuo22]

x -7 x 3 cross multiply to give -7x and 3x,then add to give the middle term which is -7x+3x=-4x ,the middle term,the factor is (x-7)(x+3)

[@Jamesdylandean]

Here is how I solved this problem. I took the -21 and realized that you had to have negative and positive multipliers to get a negative result. And so one of the combinations is seven and three. With the middle factor a negative, I decided that the seven multiplier is negative. Seven- plus three positive is negative four, so now you have the numeric part of the central factor. Since the far left factor is x squared, I broke that down to x times x. So, it comes out as x-7 times x+3. Probably did it wrong, but that is how I learned to do this.

[@Jamesdylandean]

Why the heck the line out? It is my solution, not yours. And got the correct answer, right?

[@Jamesdylandean]

As far as the logic of the lined out part, it is simple math. Negative times negative is positive. Positive times positive is positive. Only way in simple math to get a negative number is by multiplying a negative one and a positive one. Do you have a problem with that concept?

[@Jamesdylandean]

Oh, Oh should have said minus seven added to plus three equals minus four. And minus seven times plus three equals minus twenty-one. .My bad.

[@TheFashionAbuelaPatyMcGuire]

You are the best ❣️

[@awkerper]

That is so cool!

[@panlomito]

I prefer the abc-formula because the discriminator D = b² - 4ac will show the number of y=f(x)=0: D>0 then 2, D=0 then 1 and D

[@Athenaikos]

Comprehensive and detailed. Very well explained. By the way, take it from a Greek, the polynomial with 4 factors is called tetranomial, with five pentanomial, with six hexanomial and so on. Just showing off here, since we Greeks have invented math as you all know:) . Beyond, levity this was an excellent way of explaining the technique.

[@RadulovicDragan]

Greeks haven't invented math! It's been originated somewhere in the region that includes India, Persia and, later, Arabic countries. The notion of ZERO "0" was accepted in Europe in 14th and introduced into English language around 15th century. Europeans needed more than a millennia to grasp idea about ZERO "0." Greeks use of mathematics was mostly descriptive.

[@GenX4ever]

Dude. I failed algebra three times going through high school and JC. It caused me to quit school and veered me away from my path to becoming an art teacher. I ended finding a career I love but I always continued to look back in anger on Algebra. Recently started watching your videos and realized I probably had bad teachers. I wish I would have had you back then! For once in my life I think I'm starting to understand Algebra! Cheers!

[@juancatfish1]

Don't blame the teachers.

[@GenX4ever]

@@juancatfish1 Why is that exactly? Every teacher has a different teaching style. Some more suited to different learners.

[@juancatfish1]

@@GenX4ever Blame the student/teacher?

[@billschauer2240]

I would not put it like that. Effective teaching is hard. I was pretty good at math but I often found teachers sometimes explained things in such a way that I had difficulty understanding. I developed the technique of getting multiple explanations of the same subject from different sources. I did this mostly by looking how it was explained in different textbooks. I usually was able to find the other textbooks in various libraries. These days the internet makes finding other explanations much easier.

[@sundaysmith5942]

Thank you, I needed the step by step method to get me ready for algebra 2 in college for 2025

[@ChavoMysterio]

x^2-4x-21 x^2-4x+4-21-4 (x-2)^2-25 (x-2)^2-(5)^2 (x-2+5)(x-2-5) (x+3)(x-7) ✓

[@sogal4christ]

Yes long but you keep going like you do. Great

[@MrOoofah]

Once again, you address an important topic, yet your video is way too long. Being concise and efficient are good qualities in a math teacher!

[@lamper2]

YES! But in his defense he flat out tells you he's not gonna just tell you quickly how to solve it but how to UNDERSTAND how to solve it. if you got your way you wouldn't have learned for example about the case 1 vs case 2 thing

[@ellchurch7314]

I agree..

[@ellchurch7314]

I agree with Mr. Ooofah

[@alexblaze8878]

Then stop watching the video ya doofus, no one’s making you watch the entire thing. Some people would complain if their free ice cream was too cold.

[@elliottemccantsiii]

Excellent job. Thank you

[@timfurnier7061]

Sorry. You editorialize TOO MUCH! A five minute video is always fifteen minutes or more.

[@terryjohinke8065]

(x-7)(x+3) Did this in junior high in our heads. We did 100 per day ( H/wkwas to finsh.) It was pre- calculus for us.

[@vincetagleoficiar2860]

Very long time!😄

[@allanmayo9616]

Nice explanation of factoring, clear, easy to follow. Well done!

[@MrOoofah]

Please address the math problem and minimize your rambling from subject to subject.

[@achrace.profrichardachara]

Wouldn't it be simpler for those of you who don't need the extra explanations to tune off to more advanced and thus shorter tutorials?

[@vlsui66]

@@achrace.profrichardachara the teacher could have moved his "explanation" to another video and make this one focused on just the steps and answering. This video is more like "How to factorise quadratics", not "how to factorise x2-4x-21"

[@jameswarner5878]

Something I actually remembered!

[@ABC-cw7zv]

Forward to 2:35

[@williampapadopoulos8145]

(x+3)(x-7)!

[@bushtherapy7655]

X-3 x+7

[@theophonchana5025]

#QuadraticEquation #trinomial #polynomial

[@Tim-Kaa]

Nice

[@lifatnasreen33]

I like it.

[@Rubin5342]

I am deep breathing into a bag now! //ji

[@peterxoldiescheah5095]

After factoring (X-7)(X+3) Ans

[@JOKER6979]

What I don't get is why the 4x was not counted as four X. That's -4+X. I'm confused on this one.

[@tonybrock5288]

All of your videos should really be less than a minute long but somehow you manage to drag them out into this interminably long and boring Ad Revenue click bait.

[@vlsui66]

Ikr

[@keithwilson6060]

Just use the quadratic formula.

[@austindouglas268]

Was looking for this comment

[@achrace.profrichardachara]

Which is?

[@vlsui66]

Nice joke 😂😂 in this case factorising is much quicker

[@robertmeadows1657]

Libary?

[@davemcgrath6764]

Could you give me an everyday application of this?????

[@ΕΛΕΝΗΒΑ-ο7ξ]

Είναι μια δευτεροβάθμια εξίσωση βρίσκεις την διακρίνουσα και λύνεις ως προς Χ1 και Χ2 και βρίσκεις τις λύσεις τους Χ1=7 και Χ2=-3

[@Gareyp1]

3.5 min and we stlll have not even started solving the problem.

[@achrace.profrichardachara]

Isn't this only because you already know the foundations? Have you considered that there might be many perplexed people who need the conceptual foundations in order to understand the subject?

[@vlsui66]

@@achrace.profrichardachara yes but he should put that in another video, not this. Some people have come to watch this simply for the working our, steps and answer. Not for the whole context and background around this topic. This teacher could have put that in a different video- he didnt.

[@kalalukamwangala4698]

I need more time on this.

[@quabledistocficklepo3597]

I'm 84, and I was easily able to factor that (almost instantaneously) , BUT is that all there is? I had thought that finding the two terms (X-7) and (X+3) was only a step towards finding the solution. Isn't the problem finding out what number "X" stand for? Maybe it's just been too long for me, but I would appreciate an explanation. (Sat Aug , 2022) LATER: Oh, I now see that that there was nothing to solve. You didn't say that X2-4X-21 equalled something. Bear with me. What is the purpose of factoring? Suppose you had said that your expression (Is that what it's called?) equals 14. Would factoring it have helped to find the value of "X" ? If not, what is factoring for? What's the point?

[@quabledistocficklepo3597]

I know factoring. Our teacher drilled us on it, and I liked it, but how do you use it? If the problem was X2(square)-4X-21=0, then X would be 7. I got that answer by substitution/guesswork, but how would you arrive at that solution by factoring? (Old-Timer)

[@danieldennis9831]

You forgot the final step ... (X+3)(x-7)=0: x=-3 or x=7

[@michealgarcia2170]

That is a little difficult for me to figure out

[@knotwilg3596]

Your "procedure" for "trinomials" only works for the few cases where the "trinomial' is a quadratic one and where the whole numbers nicely factor in and add up. For quadratic polynomials , having the form ax²+bx+c, there IS a procedure, based on the discriminant. For "quadrinomials" of the 3rd power, there is too, but it's too laborious for most people to remember or execute. For higher powers there is no procedure, even if it happens to be a "trinomial". There are short cuts indeed, where the numbers are easy to guess, like in this case, but if you can see that, you are usually beyond the 15 minute explanation you are giving for it. So, to people who are not comfortable with elementary algebra, your video is misleading and to those who are, it is pointless.

[@bobelliott2748]

This was painful

[@vlsui66]

Ikr, way too long.

[@sergiodario58able]

I did it mentally within 10 seconds flat. It took this bloke an entire video of bla blas to come up with the result.

[@vlsui66]

Ikr, this guy takes wayy too long for a simple question

[@4everThoughtful]

He was teaching it to those who didn't know this algorithm. If you know, of course you'll be quicker and why watch?

[@sandysox]

How come all the mathematicians come out of the woodwork to teach us another way....I am a student....

[@williammaddock9179]

This guy lost me almost immediately. Sure sign of a BAD teacher.

[@dennisoyston]

Quite correct, the equation is not complete.

[@lamper2]

More likely you're a bad viewer. How many times must he explain Why he teaches the way he does? HE ACTUALLY EXPLAINS THIS IN THIS VIDEO!

[@vlsui66]

@@lamper2 no offense, but this guy takes too long to explain videos. I know some people need a lot of explaining to, but this guy seems misleading. There are other videos out there that explain just as well but take half the time. Some things this guy talked about aren't really relevant to the equation x^2-4x-21 lol

[@brooklynparker182]

Nice but I could literally factor this my is my head.

[@lamper2]

You want a gold star? perhaps you should move on to Calculus .

[@vlsui66]

@@lamper2 stop trying to prove that this teacher doesn't waste time

[@theophonchana5025]

#binomial #linearequation

[@suzannespence9636]

X-7 , x+3

[@DL101ca]

N1+N2= -4, N1×N2 = -21, so N1= 3, N2 = -7.

[@thomashoran9552]

Your explanation make it sound so hard. Making folk go back to elementary people have issues. But I love it.

[@theophonchana5025]

#factoring #factor

[@123demaio]

I skip steps and ask questions ...x+? X-?

[@dennisoyston]

Let’s Factor This Polynomial … Step-By-Step… NO THANKS!

[@theophonchana5025]

x^(2) - 4x - 21 = 0 (x - 7) (x + 3) = 0

[@dennisoyston]

But what happens if it does not =0? The equation as written in the vdeo is incorrect.

[@matthewharriman4267]

Fast forward to min 6

[@alexmclife2261]

( X + 3 ) (X - 7 ) :: X = -3 ; X = 7

[@abrahamgiliana]

Thank you, thank you, thank you. This was absolutely the best video I ever saw in algebra. I just might pay the monthly fees for your courses.

[@mulustore]

Sorry you did it. Good

[@kennethwright870]

7,-3

[@thec0untess]

Why is this a 14 minute video

[@vlsui66]

Ikr

[@sharondavidson6675]

I'm confused

[@dennisoyston]

Please, don't be confused. Math is exciting. It is people like this that are there to confuse you. As long as you can count the correct change when you go shopping then you are OK. L&K D.

[@b213videoz]

(x-7)(x+3) = 0 😊

[@billm3210]

bit confusing way to teach kids. Good explaination but easier method is getting the factors and using two sided equation which becomes easier.

[@vlsui66]

Ikr

[@kimngo5197]

x = 7 and x = - 3

[@jhessperez759]

its take too much explanation,it wasted much time..

[@vlsui66]

Ikr, way too long

[@SILICONALI420001]

Actually Algrebra was invented by moors(Arabs/ muslims)

[@tamexgemechu1471]

1oq Ur teaching techniques attractive 1

[@gregjohnson720]

Please excuse me for being pedantic but did you say “ my complete math LIBARY or my complete math LIBRARY”? If you said LIBARY, you might want to brush up on your English language pronunciation.

[@danieldennis9831]

Or you were just asking for the factors and it's my bad.

[@soumitra0505]

(X-7)(x+3)

[@harrymatabal8448]

14 minutes to explain this

[@theophonchana5025]

x - 7 = 0 x = 7

[@kurtlindal4801]

You are making the answer much to hard to understand. Anyone who has reached the level of being expected to factor a trinomial already knows what they are, so drop the crap and just show whats needed ie: terms that sum to equal the second term (-4) and multiply to equal the third term (-21). It took my math 10 teacher all of 10 minutes to make sure our entire class understood the process. Only when the first term has a constant greater than 1 is the problem at all difficult to factor.

[@omincat2703]

I need to figure out what to do if its not just x² and a number bigger than one

[@theophonchana5025]

x + 3 = 0 x = -3

[@m802001]

I get X=7 and X=-3 using the quadratic equation and I don’t know what I’m doing wrong. Google seems to agree with me. Help!

[@royrice8597]

Let’s not…………