anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
@ospreytriple
anonymous
  • anonymous
Is it\[2xy ^{4} + 2x ^{2y} - 3y ^{2} + 10x ^{3}\]
anonymous
  • anonymous
Or maybe\[2xy ^{4} + 2x ^{2}y - 3y ^{2} + 10x ^{3}\]

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
I'm having difficulty understanding the question. Is the given expression one of the ones I wrote above?
anonymous
  • anonymous
the seconf one is what they gave me.
anonymous
  • 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
  • anonymous
nope lol
anonymous
  • anonymous
No problem. Do you know what a term is? How many terms are there in the given expression?
anonymous
  • anonymous
4?
anonymous
  • anonymous
That's right. Very good. In an algebraic expression, terms are separated by plus and minus signs.
anonymous
  • 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
  • anonymous
Which term has the highest exponent of x?
anonymous
  • anonymous
2xy to the power of 4
anonymous
  • 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
  • anonymous
So, think of it like\[2x ^{1}y ^{4}\]
anonymous
  • anonymous
yeah
anonymous
  • anonymous
So which term has the highest exponent of x?
anonymous
  • anonymous
so 3y to the power of 2?
anonymous
  • 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
  • anonymous
10x to 3?
anonymous
  • anonymous
That's the one. So that term has to come first. Which term comes next?
anonymous
  • anonymous
3x to 2?
anonymous
  • anonymous
There is no such term in the given expression. Look closely.
anonymous
  • anonymous
oh 3y to 2
anonymous
  • 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
  • anonymous
All you should be concerned with is the exponent of the x.
anonymous
  • 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
  • anonymous
0
anonymous
  • anonymous
Nope. Remember when there no numbered exponent, it is assumed to be ...?
anonymous
  • anonymous
this is so hard!!!!
anonymous
  • 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
  • anonymous
yeah
anonymous
  • 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
  • anonymous
yeah
anonymous
  • 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
  • anonymous
okay
anonymous
  • 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
  • anonymous
1
anonymous
  • anonymous
Bravo! Now you're getting it. The second term is\[2x ^{2}y\]What's the exponent of x?
anonymous
  • anonymous
2
anonymous
  • anonymous
Yayy! The next term is\[3y ^{2}\]What is the exponent of x? Tricky. Be careful.
anonymous
  • anonymous
0
anonymous
  • anonymous
I'm so proud of you! And the last term is\[10x ^{3}\]What's the exponent of x?
anonymous
  • anonymous
0
anonymous
  • anonymous
Oops. Have another look.
anonymous
  • anonymous
ohh 2
anonymous
  • anonymous
Almost. Check again.
anonymous
  • anonymous
3 srry i dont have my contacts in
anonymous
  • 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
  • anonymous
10x*3+2xy*4+2x*2y-3y*2
anonymous
  • anonymous
Close. Check out the second and third terms. Are they in the right order?
anonymous
  • anonymous
no? swap them
anonymous
  • anonymous
That's right. 2xy^4 has a x-exponent of 1 while 2x^2y has an x-exponent of 2. Understand?
anonymous
  • anonymous
yeah
anonymous
  • anonymous
Ok. So re-order those terms and you'll have your answer.
anonymous
  • anonymous
Want to practice identifying exponents for a couple of minutes to reinforce this?
anonymous
  • anonymous
the answers are either 1 2 3 or 5
anonymous
  • 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
  • anonymous
2?
anonymous
  • anonymous
The whole term?
anonymous
  • anonymous
they dont give the whole thing as options just 1 2 3 5
anonymous
  • anonymous
I know. But we need to examine the whole term to determine what degree it is. So what is the 3rd term?
anonymous
  • anonymous
2x*2y
anonymous
  • anonymous
Nope. That's the 2nd term. What's the third?
anonymous
  • anonymous
2xy*4
anonymous
  • anonymous
Right on. Do you know what degree means?
anonymous
  • anonymous
nope
anonymous
  • 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
  • anonymous
nope lol
anonymous
  • anonymous
Add the exponents of the x and y together to get the degree.
anonymous
  • anonymous
would it be 3 then?
anonymous
  • anonymous
In\[2xy ^{4}\]what is the exponent of the x? what is the exponent of the y? add them together
anonymous
  • anonymous
5
anonymous
  • anonymous
Hooray. The degree of that term is 5. There's your answer.
anonymous
  • anonymous
finally thank you!! lol
anonymous
  • anonymous
You're welcome. Practising identifying the exponents of variables and determining the degree of terms will make it seem much easier.
anonymous
  • anonymous
Keep up the hard work

Looking for something else?

Not the answer you are looking for? Search for more explanations.