How to Divide a Polynomial by a Binomial Using Long Division

[Googl]

Hi all,

Please help understand how this works out. I know how to work it out when 3x-1 has no 3 ie: x-1.

Divide

$$x^3+4x^2+3x$$ by $$3x-1$$

Thank you

 

[SteamKing]

What factor multiplied by 3x equals x^3? That is,

If x^3 = 3x * Z, what must Z equal?

 

[Integral]

Please show us some effort on your part.

 

[Curious3141]

I'm assuming you're using synthetic division? Show us how you would divide that polynomial by $\displaystyle x - \frac{1}{3}$.

 

[Googl]

Hi,

What I have posted is actually part of the question. This is not homework. I have worked through the all question, I forgot to mention that I was stuck at that point and gave it a lot of thought but could not think through it.

 

[Googl]

What factor multiplied by 3x equals x^3? That is,

If x^3 = 3x * Z, what must Z equal?

Because I have not really came across a problem like this I am finding it even difficult to think about the factor. An example will enlighten me. How about powering it

$$(3x)^3$$

and divide by 9.

$$(3x)^3 / 9$$

That would not work, would it?

 

[verty]

If it make it easier, multiply the dividend by 3, then divide, then remember to divide by 3 at the end.

-- I use this trick with matrices a lot.

 

[Googl]

If it make it easier, multiply the dividend by 3, then divide, then remember to divide by 3 at the end.

-- I use this trick with matrices a lot.

Hi,

I have tried that but it won't work without leaving decimals/fractions. I will am using long division.

 

[verty]

Right, then do it the proper way according to the method you have learned, which is what SteamKing pointed out.

 

[Googl]

Is there a way of working it out without getting fractions when using long division? I know the factor will be:

$$(x)^2 / 3$$

 

[HallsofIvy]

Why would you NOT want to get fractions?
I suppose you could use "0.333333..." but that would be silly. "3x" divides into $x^3$ $x^2/3$ times. That is as easy as you can write it.

 

[symbolipoint]

If you have a good understanding how ordinary long division works, this example of yours works the same way, and may be easier.

What I begin to describe here is NOT synthetic division.

You want $$x^3+4x^2+3x$$ divided by $$3x-1$$.

What is $$x^3$$ divided by $$3x$$?
Put this result above the dividend term of x^3. Multiply the entire divisor 3x-1 by your just found result, and write this under the first two terms of the dividend and subtract. Bring down the next term.
Now, what is the leading term you find after the subtraction divided by 3x?

..
You would continue the process. Is the description enough for you to finish this to completion? You may or may not have a remainder.

This is much easier to do on paper than through this text based system for typing.( I KNOW the tags are right. TEX is failing again)