Question

@eSpeX Can you explain polynomials to me? My lesson on it complicates it so much.

Answer 1

What is giving you trouble?

Answer 2

I don't even know how to do the problem, pretty much. And I don't have enough time to read the whole lesson, so I need a simple explanation.

Answer 3

A polynomial is not a "problem" as much as it is a way to describe a term within an expression.
3x is a polynomial, 5+x is a polynomial, x^2 is a polynomial. Do you have a particular problem that you need assistance with or was it just the definition?

Answer 4

I have three, actually.

Answer 5

Well, we can look at them and see if there isn't some way to clear up the confusion.

Answer 6

1. 8a – 5
2. 3x + y + z
3. 6x^2

Answer 7

Okay, and what are you asked to do with these?

Answer 8

classify each one by degree and number of terms.

Answer 9

@eSpeX

Answer 10

The degree of the polynomial is determined by the highest power, so your #3 would be a second degree polynomial.

Answer 11

Okay, how would I know what is the highest power?

Answer 12

Whichever expression has the largest exponent.

Answer 13

If you have:
x^3 + x
y^2 + y^8

which of those expressions is the higher degree?

Answer 14

The second one, right?

Answer 15

@amistre64 ?

Answer 16

Correct, because it contains the term with the highest exponent.

Answer 17

So what degree are the three of yours?

Answer 18

The other ones don't have exponents. .-.

Answer 19

Actually it does. \[x \rightarrow x^{1}\] just like \[5 \rightarrow 5x^{0}\]

Answer 20

The second one is a 5th degree trinomial? I'm not suree... the third one was a second degree polynomial, right?

Answer 21

http://bit.ly/18LGI5L

Answer 22

Your first and second expressions are 1st degree because the largest exponent is 1.Your third expression is a 2nd degree because it has an exponent of 2.

Answer 23

8a – 5 (First degree Binomial)
3x + y + z (First degree Binomial)
6x2 (Second degree polynomial)
Like this? @eSpeX

Answer 24

Precisely. Then you just need to order them by number of terms.

Answer 25

So, the second one would be first, the first one would be second, and the third one would just stay third, right?

Answer 26

@satellite73 @amistre64 ?

Answer 27

@dmezzullo ?

Answer 28

@Compassionate Heeeelp. :c

Answer 29

What do you need help with?

Answer 30

Read the previous conversation, silly.

Answer 31

Tsk. Rotten luck. Alright.

Answer 32

A mononomial has one term. The prefix: Mono, means 1.
[e.g., 5x]

A binomial has two terms. The prefix: Bi, means 2.
[e.g., 5x + x]

A trinomial has three terms: The prefix: Tri, means 3.
[e.g., 5x + x + y]

Now, a Polynomial is just the general outline for all three types (mono, bi, and tri) all fall into the classification of a Polynomial. Even things with 5, 10, or 100 terms fall into the classification: Polynomial.

The reason for this is it's hard to memorize a whole bunch of prefixes.
If I had an expression with ten terms in it
[e.g., x + y + a + g + f + h + t + e + w + a] I could call it a decinomial
Or one with four terms
[e.g., 2x + 2y + 2h + 3x] I could call it a quadranomial.

But likeI said, memorizing all these prefixes are a waste of time. So we just call them polynomials.

[See attachment 1 now]

------------------------------------
The degree is just the highest exponent.

Classifying polynomials is easy.
If I had: \[2x + x^5\]
I would say: This is a binomial of teh 5th power.

If I had: \[x + y + y^2\]
I would say: This is a trinomial to the 2nd power.

If I had: \[x + y + w + s + h + u^2\]
I would say: This is a Polynomial to the 2nd power

Answer 33

So, is what I had so far correct?

Answer 34

@hartnn

Answer 35

8a – 5 (First degree Binomial)
3x + y + z (First degree Binomial)
6x2 (Second degree polynomial)

1. Yes

2. Wrong. First degree TRInomial. There are THREE terms.

#. Wrong. Second degree MONOnomial. It has ONE term.

Anything with more than THREE terms is classified as a POLYNOMIAL.

Answer 36

Okay, can you help me with Part 2?

Answer 37

Which is?

Answer 38

@Compassionate

Answer 39

Oh, oops. Hold on.

Answer 40

I'm helping people in physics. So I can't come to your rescue right a way...

Answer 41

Sorry, I'm in a hurry.

Answer 42

The first one is.

The secondone isn't.

Standard form descends from the highest power. If the powers are the same, then you descend the power with the highest coefficient.

\[10xy^4 - 6x^2y - 8x^2y^2\]

Answer 43

I have to go. Goodbye.