Arrange the following polynomial into descending order for x, then interpret the degree of the 3rd term.
2xyto the power of 4 + 2xto the power of 2y − 3yto the pwer of 2 + 10xto the power of 3

- anonymous

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- anonymous

@ospreytriple

- anonymous

Is it\[2xy ^{4} + 2x ^{2y} - 3y ^{2} + 10x ^{3}\]

- anonymous

Or maybe\[2xy ^{4} + 2x ^{2}y - 3y ^{2} + 10x ^{3}\]

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## More answers

- anonymous

I'm having difficulty understanding the question. Is the given expression one of the ones I wrote above?

- anonymous

the seconf one is what they gave me.

- anonymous

OK. What the question asks you to do is to arrange the terms of the expression in descending powers of x. Can you do that?

- anonymous

nope
lol

- anonymous

No problem. Do you know what a term is? How many terms are there in the given expression?

- anonymous

4?

- anonymous

That's right. Very good. In an algebraic expression, terms are separated by plus and minus signs.

- anonymous

So for each of the four terms, look at the exponent of x. Arrange the terms from the highest to the lowest exponent of x. What do you think?

- anonymous

Which term has the highest exponent of x?

- anonymous

2xy to the power of 4

- anonymous

Not quite. In\[2xy ^{4}\]the 4 is the exponent of y. The exponent of x is 1. Remember that when there is no numbered exponent, it is assumed to be 1. Make sense?

- anonymous

So, think of it like\[2x ^{1}y ^{4}\]

- anonymous

yeah

- anonymous

So which term has the highest exponent of x?

- anonymous

so 3y to the power of 2?

- anonymous

No. In this term, x doesn't even appear, so it has an exponent of 0. Think of it like\[3x ^{0}y ^{2}\]Try again.

- anonymous

10x to 3?

- anonymous

That's the one. So that term has to come first. Which term comes next?

- anonymous

3x to 2?

- anonymous

There is no such term in the given expression. Look closely.

- anonymous

oh 3y to 2

- anonymous

But recall that there is no x, so it's exponent is zero. Think of it like\[3x ^{0}y ^{2}\]For this question, forget about the exponent of y. The y's are just along for the ride. The question asks you to order the terms based on the exponent of the x. That's all.

- anonymous

All you should be concerned with is the exponent of the x.

- anonymous

Let's try looking at it a from a different angle. The first term in the expression is\[2xy ^{4}\]What is the exponent of the x in this term?

- anonymous

0

- anonymous

Nope. Remember when there no numbered exponent, it is assumed to be ...?

- anonymous

this is so hard!!!!

- anonymous

You're doing fine. With some practice, you'll see how easy it is. Any variable (or number) without an exponent written has an exponent of 1. For example\[x=x ^{1}\]\[y=y ^{1}\]\[4=4^{1}\]and so on. If there is no exponent written, it is assumed to be 1. That OK?

- anonymous

yeah

- anonymous

For another example, in the term\[5xy ^{3}\]the exponent of the 5 is 1 (because there's no written exponent)
the exponent of the x is also 1 (because no exponent is written)
and the exponent of the y is 3
Get it so far?

- anonymous

yeah

- anonymous

The other rule about exponents that we need for this question is that the value of any number raised to the exponent zero is 1. Mathematically\[x ^{0}=1\]\[y ^{0}=1\]\[2^{0}=1\]. OK?

- anonymous

okay

- anonymous

Good. We have all the tools we need. So let's look at the first term again\[2xy ^{4}\]What is the exponent of x?

- anonymous

1

- anonymous

Bravo! Now you're getting it. The second term is\[2x ^{2}y\]What's the exponent of x?

- anonymous

2

- anonymous

Yayy! The next term is\[3y ^{2}\]What is the exponent of x? Tricky. Be careful.

- anonymous

0

- anonymous

I'm so proud of you! And the last term is\[10x ^{3}\]What's the exponent of x?

- anonymous

0

- anonymous

Oops. Have another look.

- anonymous

ohh 2

- anonymous

Almost. Check again.

- anonymous

3 srry i dont have my contacts in

- anonymous

There you go. Now put these four terms in order from the highest exponent of x to the lowest. Don't forget...the sign (+ or -) has to go with the term.

- anonymous

10x*3+2xy*4+2x*2y-3y*2

- anonymous

Close. Check out the second and third terms. Are they in the right order?

- anonymous

no? swap them

- anonymous

That's right. 2xy^4 has a x-exponent of 1 while 2x^2y has an x-exponent of 2. Understand?

- anonymous

yeah

- anonymous

Ok. So re-order those terms and you'll have your answer.

- anonymous

Want to practice identifying exponents for a couple of minutes to reinforce this?

- anonymous

the answers are either 1 2 3 or 5

- anonymous

Oh. Sorry, you're right. I had to go back and read the original question. So, now that the terms are all in the correct order, the question wants to know what the degree of the third term is. OK. So what is the third term when they're all in order?

- anonymous

2?

- anonymous

The whole term?

- anonymous

they dont give the whole thing as options just
1
2
3
5

- anonymous

I know. But we need to examine the whole term to determine what degree it is. So what is the 3rd term?

- anonymous

2x*2y

- anonymous

Nope. That's the 2nd term. What's the third?

- anonymous

2xy*4

- anonymous

Right on. Do you know what degree means?

- anonymous

nope

- anonymous

It's simple. The degree of an algebraic term is the sum of the exponents of ALL the variables in the term. Can you do that?

- anonymous

nope lol

- anonymous

Add the exponents of the x and y together to get the degree.

- anonymous

would it be 3 then?

- anonymous

In\[2xy ^{4}\]what is the exponent of the x?
what is the exponent of the y?
add them together

- anonymous

5

- anonymous

Hooray. The degree of that term is 5. There's your answer.

- anonymous

finally thank you!! lol

- anonymous

You're welcome. Practising identifying the exponents of variables and determining the degree of terms will make it seem much easier.

- anonymous

Keep up the hard work

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