Can anyone explain dividing polynomials? Pleeaasseee :(

Question

imstuck · Answer

The long way or using synthetic division?

anonymous · Answer

Ummm well what's that? :/

imstuck · Answer

is there a certain way that you HAVE to know how to use?  Or are you just wanting to divide and get the job done?  I can teach you either way

anonymous · Answer

Whichever would be the quickest and easiest way.

imstuck · Answer

The easy way or the more difficult way?

imstuck · Answer

Ok, then synthetic is definitely the way to go.  Do you have a polynomial you are wanting to divide by another polynomial, or something?  Depending upon what your divisor is, you may not be able to use synthetic.  Show me what you need to divide out.

anonymous · Answer

Okay so I guess we'll just start with an easy one and go from there, what if we had
(12a^5b^3)/(8ab^2)

imstuck · Answer

Do you mean this:

imstuck · Answer

$$\frac{ 12a ^{5}b ^{3} }{ 8ab ^{2} }$$

anonymous · Answer

Yeah :)

imstuck · Answer

Ok, you don't need synthetic here because you are not dividing a polynomial by a binomial.  this is a case of pure simplification.

anonymous · Answer

Okay

imstuck · Answer

First reduce between the 12 and the 8.  8 doesn't go into 12 evenly, but they are both even numbers so they can be divided by 2 down til they can't be reduced any further.  12 reduces to 6 which reduces to 3 which cannot be reduced any further.  8 can be reduced to 4 which can be reduced to 2 which cannot be reduced any further, so the numbers part looks like this now:

imstuck · Answer

$$\frac{ 3a ^{5}b ^{3} }{ 2ab ^{2} }$$

anonymous · Answer

Right! So first simplify everything, gotcha.

imstuck · Answer

Then reduce between the a on the top and the a on the bottom.  There is one on the bottom of the fraction, so that one would cancel out and take 1 in the top with it when it goes.  So now you have:$$\frac{ 3a ^{4} b ^{3}}{ 2b ^{2} }$$

imstuck · Answer

Now reduce between the b on the top and the b on the bottom.  You have a b squared on the bottom and a b cubed on the top. The basic rule for exponents is that you subtract the power of b in the bottom from the power of b on the top, like this:

imstuck · Answer

$$b ^{3}-b ^{2}=b ^{3-2}=b ^{1}=b$$

imstuck · Answer

So now the b's in the bottom are gone and you have one left on top.  So that whole thing reduces to $$\frac{ 3a ^{4} b}{ 2 }$$

imstuck · Answer

That's more simplification than division.

anonymous · Answer

and it can't be simplified further, so we're done?

igreen · Answer

Yes, that's correct @LearningIsAwesome

anonymous · Answer

So then if instead we had, let's say, $$12b^2/3b$$

igreen · Answer

Same old, same old..

$\dfrac{12b^2}{3b}$

anonymous · Answer

First we divide the numbers, so it's $$4b^2/b$$

anonymous · Answer

then the variable, making it 4b, because of the understood exponent of 1?

igreen · Answer

3 can get into 12..so we have:

$\dfrac{4b^2}{b}$

Now for the variables:

$b^2 - b^1 \rightarrow b^{2-1} \rightarrow b^1 \rightarrow b$

igreen · Answer

Yes, you got it.

igreen · Answer

Which leaves us with..?

anonymous · Answer

4b

igreen · Answer

Yes. :)

anonymous · Answer

Awesome! So, what would be the next step in learning how to divide any polynomials? @iGreen What would be something just a little more complicated?

igreen · Answer

Dividing a trinomial by a binomial is a long ..

anonymous · Answer

Can you give an example? I can make another question for ya and tag you on it so you can get all them medals haha

igreen · Answer

Okay, sure.