Organize the following polynomial expressions from least to greatest based on their degree:

I.x + 2xyz
II.3x + y + z
III.2x3y + y2x - 3x + 4
IV.9x3yz

II, III, I, IV
III, I, IV, II
I, II, IV, III
II, I, III, IV

Question

Organize the following polynomial expressions from least to greatest based on their degree:


I.x + 2xyz
II.3x + y + z
III.2x3y + y2x - 3x + 4
IV.9x3yz

 II, III, I, IV 
III, I, IV, II
 I, II, IV, III 
II, I, III, IV

anonymous · Answer

@arabpride @sleepyjess @Godlovesme

anonymous · Answer

@HelpBlahBlahBlah @pooja195 @piercetheveil47

anonymous · Answer

Please help!

e.mccormick · Answer

Do you know how to find the degree of a polynomial?

anonymous · Answer

No.

anonymous · Answer

I think it is C?

e.mccormick · Answer

For a SINGLE variable, like $x^2+x+1$ it is the degree of the highest term.  So 2 in this example.

For a multivariable, like $x^2y$ it is all the fegrees added together.  So 3 in this example.

anonymous · Answer

Okay? So its C?

e.mccormick · Answer

Now, there is one other thing on multi variable... the highest is on a per term basis, so $x^2y+x$ is still just 3.

e.mccormick · Answer

I have not looked at yours yet...

anonymous · Answer

What do you mean?

e.mccormick · Answer

What do I mean about which part?

anonymous · Answer

So we are just putting the amount of terms fromleast to greatest?

e.mccormick · Answer

The degree.

e.mccormick · Answer

$x^9$ is the 9th degree becaue the power is 9.

anonymous · Answer

@arabpride Please help...
I dont get it...

anonymous · Answer

i g2g its getting late. Thank you for trying to help...

e.mccormick · Answer

$x+y$ is the first degree because each term only has a degree of 1.
$xy+1$ is the 2nd degree because the highest term has a degree of 2.
$x+x^2+1$ is 2nd degree because the highest term has a degree of 2.

anonymous · Answer

Okay?

anonymous · Answer

So then it would be B?

e.mccormick · Answer

The degree relates to the multiplcation of variables.  So if I look at:

$x^3y$ it is the same as $xxxy$ 4 variable, 4th degree.

$x^3y+x$ it is the same as $xxxy+x$ 4 variables in the term with the most variable, so still 4th degree.

e.mccormick · Answer

So lets take them in order, rather than guessing.

What is the degree of: x + 2xyz  ?

anonymous · Answer

umm? 4?

anonymous · Answer

Am i wrong again? *sigh*

e.mccormick · Answer

Well, thing of it as:
x + 

and

2xyz 

seperated.  Which one has the most variables?

anonymous · Answer

That 1 term. Right?

e.mccormick · Answer

And everybody gest things whrong untill they really understand it... then they just get it wrong less often.  =)

anonymous · Answer

Okay. Thanks for the tip! :)

e.mccormick · Answer

Most... the 2xyz,  it has $x^1$ and $y^1$ and $z^1$.  So that is 3 variables all to 1 power, which makes that 3rd degree.

e.mccormick · Answer

OK, so  I.x + 2xyz is 3rd degree.  Now, lets see if you do a little better with:

II.3x + y + z 

Remember, you are just looking at each term seperatly (a term is seperated by a + or a -)

anonymous · Answer

2 terms.

anonymous · Answer

No 3... Sorry.

e.mccormick · Answer

Well, that is correct!  It has 3 terms.  But which has the highest degree, or power?  We are looking for degree =)  But I am glad you got the number of terms correct.

anonymous · Answer

Okay umm 3x got the greaest. I think...

e.mccormick · Answer

Yes... but not because of the 3.  To be honest, it is a bit of a trick.  They all have the same power... 1.  So 1st degree.

anonymous · Answer

Oh. Okay.

e.mccormick · Answer

OK, this one has 4 terms:
III.2x3y + y2x - 3x + 4 

Now, I am betting thatis supposed to be:

III.$2x^3y + y^2x - 3x + 4 $

All you want is the term with the highest total of the powers.  That is the degree.

e.mccormick · Answer

Obviously it is not 4.  No variable, so degree 0.  And a little looking and that 3x just has an x so degree of 1, not that high.  But $2x^3y$ and $y^2x$ look promissing.  Can you figure out which of them sets the degree and what the degree is?

anonymous · Answer

2x^2y

e.mccormick · Answer

$\Large 2x^3y$    Yep!  Which is also $2xxxy$ because of the $x^3$ so what is the degree?

anonymous · Answer

5? or 4?

e.mccormick · Answer

4.  3xes + 1 y = 4th degree.  I think you are finally beginning to see this.

OK.  So.  

IV.$9x^3yz$

What is the degree of that?

anonymous · Answer

3?

e.mccormick · Answer

Remember, there is more than one x.  Count all the xes, then add the y and z.

anonymous · Answer

5?

e.mccormick · Answer

Woowoo!  Yep.

anonymous · Answer

YAY!

e.mccormick · Answer

So:
I.$x + 2xyz$ is 3rd degree
II.$3x + y + z$ is 1st degree
III.$2x^3y + y^2x - 3x + 4$ is 4th degree
IV.$9x^3yz$ is 5th degree

e.mccormick · Answer

So what is the oder from lowest to highest degree?

anonymous · Answer

So its D!?

e.mccormick · Answer

=)

anonymous · Answer

THANK YOU SOO MUCH!!! I get it a bit more.

e.mccormick · Answer

And that is how we learn.  In little bits.  So find some more to practice and a littl here and there and you will get it.

anonymous · Answer

Thank you! :)