Remainder Theorem and Factor Theorem

[farahroslend]

@supersanya10 The function cannot be factorised because the factorised version of your function does not satisfy the original version of your function, when x=1.

[farahroslend]

@supersanya10 according to the factor theorem, (x-1) is not a factor of the function you mentioned. This is because when the x=1, the function does not gives zero. Thus, the function cannot be factorised.

[supersanya10]

I have a question: Say the problem was "is (x-1) a factor of x^456-3x^300+x^5+2? How am I supposed to proceed with this? The exponents are not consecutively decreasing: it goes 456,300,5, how am I supposed to proceed? PLEASE HELP!! Thank you

[Safijah]

If you zoom out to about 50%, the video quality s better

[ooVEXoo]

great video! thanks!

[jono1478]

Good tutorial , but poor video quality.

[PiwiTeen]

my math teacher sux :'(

[ArcDemyx]

Thank you soooo much for the help!

Now what if the question asks to Identify any restrictions on the variable? is that the same as finding the domain? if so, how do you do that?

[HowlBlack]

Thank you so much. I was completely lost when I was first showed this.

[sonudevu]

since the theorem states that " if a polynomial, say p(x) is divided by a linear polynomial (x-a), then the remainder is p(a)"  why merely talking opposite sign? Instead u can take (x+2) as [x-(-2)] so that the statement of the theorem remains intact.

[minkusbc]

@sonudevu You are absolutely correct, and I usually do show that to students as a reason why you take the opposite. However, if you start changing things all from (x + 2) to (x - (-2)) then I have found that you lose half of the class. It is always a toss up about how far you go in the "theory" part of the lesson, before you show them what just "works". Your point is well taken though.

[Bapbs89]

This helped a lot. Thank you!

[milk4lifez]

OHHHH THE OPPOSITE OF THAT SIGN OHHHHH THANK YOU

[Cerrrline]

I love you. My math teacher can't teach for nuts.

[mcpimpen]

damn this isnt he remainder theorem for calc 2 lol :(

[akbar2k7]

Hi are you American if so please enlighten me on the American education system because at what age would you learn Polynomials , Binomial Theorems, complex Co-ordinate Geometry Circles Etc., Advanced Trigonometry eg.Identities of functions etc. and Calculus the basics polynomial integration and differentiation. Because in the UK that would come in the A -levels usually taken from the age of 16-18 I myself along with a few other boys the top 5% can take a course which covers it at the age15-16.

[SkittlesClubFtw]

Thank you SO much! Your math videos have really helped me a lot. You have a very simplistic way of explaining, which makes it easier to understand! Thanks. =)

[metalgeorge123]

okay, but how do you solve the equation (that is equal to zero) when you have got the factor?

something like....

(equation) = (factor) (ax^2 + bx + c)

[frohzen]

@metalgeorge123

then you just factorise the quadratic section of the function which shud result in another 2 factors. Being a degree 3 polynomials to start, means you should end up with 3 factors or 'x intercepts'.(though u may get a square factor or cubed factor meaning you will have 2 or one intercepts)

[WePrank4Fun]

u didnt put minus 2 into the brackets. did u say that the factor was (x-2) to make it +2?

[LilKris00]

thanks, this was very helpful :D

[jackcg04]

Thanks alot, this helped a bunch

[Timmehhh100]

There is absolutely no difference between the the two theorums; factor theorum is just remainder theorum, but where the remainder is 0...

[minkusbc]

You're correct. When a theorem is just a special case of another theorem, sometimes it is called a "corollary". So the factor theorem is a special case or corollary of the reaminder theorem.

[temoor555]

Remainder theorem and Factor theorem are related. But, it is wrong to say they are absolutely the same. Consider a polynomial P(x) divided by a linear function, x-b. Remainder theorem, explains a "relation" that exists between the constant b in linear function, x - b, and the remainder R, which is produced as a result of division.

Factor theorem on the other hand, defines the "condition" when a function is a factor of another function.

[ILoveGirlsAloud61]

Thankyou soooo much!

[ILoveGirlsAloud61]

I've done my homework wooo! =D

[mk2hot4dis]

why do u change the signs?

[The12thAkatsuki]

Because it's like a root of that polynomial and you're solving for x. For example, if x -2 = 0, then x = 2. So you find f(2). Another example: If you want to find the remainder when you divide any polynomial by (5x - 3), then you could say, (5x - 3) = 0. Then x would be 3/5. So you find f(3/5) and that would give you the remainder! REMEMBER: It only works when it's linear, like (5x - 2) or (x + 4). If you want to find the remainder when you divide any polynomial by (x^2 + 3x - 2), ...

[The12thAkatsuki]

... Then you can't just simply solve for x and do this thing. You would have to use the long division to divide the whole thing and figure out the remainder. I hope this helps, although it was pretty long !!

:P

[mk2hot4dis]

Oh no that was great! Thanks!

[ieatpie19]

wow that was explained so clear thank you@!

[mrjohan27]

Thanks a lot man, now I got it. You're better than my professor who spend 50 mins explaining this and I don't understand at all.

[gamerjr92]

Any chance you can explain to my why the remainder theorem works. Its just a habit of mine having to know how everything works not just that it does. i get everything fine though.

[exce11er]

good habit

[123hoythere]

i wish i had that habbit

[Dilpil01]

thanks for making this simpler

[muchahco1]

i owe u

[muchahco1]

ur the best

[seekluv]

thanks from student of glendale college calif, i understand it better now. I kind of understood it before, so i'm not like all these other numskulls..... :)ha ha just joking other people, don't beat me up.

[soujiro32]

Awesome! TY DUDE!

[bigboy1091]

cheers mate.

[AlbertoOfSpain]

dude, you're my hero! this stuff has been very confusing to me but you saved me! i really learned what in class i don't

[5h0r7ii3]

thank you! i enjoy your videos a lot!

i come home from school to watch your videos on stuff i have learned in class to review!

your videos help me a lot, you are a great teacher! i hope you keep posting up videos!

[brandonrevelli]

your a great teacher, and iv watched a few of your videos and honestly i wish youd come out of retirment

[myles1428mjc]

thankd bud had a test tomarow and this helped

[myles1428mjc]

thankd bud had a test tomarow and this helped

[LaigibaMik]

THANK YOU!!!