Question

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

Answer 1

@ospreytriple

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

the seconf one is what they gave me.

Answer 6

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?

Answer 7

nope
lol

Answer 8

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

Answer 9

4?

Answer 10

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

Answer 11

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?

Answer 12

Which term has the highest exponent of x?

Answer 13

2xy to the power of 4

Answer 14

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?

Answer 15

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

Answer 16

yeah

Answer 17

So which term has the highest exponent of x?

Answer 18

so 3y to the power of 2?

Answer 19

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.

Answer 20

10x to 3?

Answer 21

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

Answer 22

3x to 2?

Answer 23

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

Answer 24

oh 3y to 2

Answer 25

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.

Answer 26

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

Answer 27

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?

Answer 28

0

Answer 29

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

Answer 30

this is so hard!!!!

Answer 31

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?

Answer 32

yeah

Answer 33

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?

Answer 34

yeah

Answer 35

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?

Answer 36

okay

Answer 37

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?

Answer 38

1

Answer 39

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

Answer 40

2

Answer 41

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

Answer 42

0

Answer 43

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

Answer 44

0

Answer 45

Oops. Have another look.

Answer 46

ohh 2

Answer 47

Almost. Check again.

Answer 48

3 srry i dont have my contacts in

Answer 49

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.

Answer 50

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

Answer 51

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

Answer 52

no? swap them

Answer 53

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

Answer 54

yeah

Answer 55

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

Answer 56

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

Answer 57

the answers are either 1 2 3 or 5

Answer 58

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?

Answer 59

2?

Answer 60

The whole term?

Answer 61

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

Answer 62

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

Answer 63

2x*2y

Answer 64

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

Answer 65

2xy*4

Answer 66

Right on. Do you know what degree means?

Answer 67

nope

Answer 68

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?

Answer 69

nope lol

Answer 70

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

Answer 71

would it be 3 then?

Answer 72

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

Answer 73

5

Answer 74

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

Answer 75

finally thank you!! lol

Answer 76

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

Answer 77

Keep up the hard work