Remainder Theorem and Factor Theorem

Introduction to the Remainder Theorem and its partner, the Factor Theorem. This is video 30 of 51 in the solving equation series. The next three series are "Word Problems", "Factoring" and "Graphing".

Category:

Howto & Style

Tags:

• mathematics
• equations
• solving
• series

[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.

[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.

[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.