Question

What is the classification of this polynomial?

-4x^2y^2-2y+6y^3

Answer 1

:/

Answer 2

It is 3rd degree due to the highest power being to ^3

Answer 3

Isn't a monomial one term?? O.o

Answer 4

don't monomials have one term?

Answer 5

Yes i messed up -facepalm-

Answer 6

:)

Answer 7

I know theres monomials=1 binomials=2 and trinomial=3 but I don't/never herd of 4 term name

Answer 8

maybe quadrinomial

Answer 9

I looked that up

Answer 10

is it only 3 terms because they are multiplied?

Answer 11

Isn't everything 4 and up a polynomial? or something?

Answer 12

yeah i think its just polynomial

Answer 13

and i have to go sorry, yay for title

Answer 14

How many terms?
All you need to do is to see how many parts are separated by plus signs and minus signs.

\(-4x^2y^2\color{red}{-}2y\color{red}+6y^3\)

3 parts, so 3 terms

Answer 15

That means it's a trinomial.

Answer 16

third degree trinomial

Answer 17

Okay

Answer 18

oh you are soooo right. It's a trinomial. Good catch @mathstudent55 !

Answer 19

Next is the degree.
First, you need to find the degree of each term.
To do that, add the exponents of the variables of each term.
Keep in mind that a plain variable is the same as degree 1, since \(x = x^1\)

Answer 20

\(\large -4x^\color{red}2y^\color{red}2-2y^\color{blue}1+6y^\color{green}3\)

Add the red numbers. 2 + 2 = 4
Add the blue numbers (there is only one, so it's 1)
Add the green numbers (again, there is only one number, so it's 3)

The degrees of the terms are: 4, 1, 3

Ok so far?

Answer 21

Right

Answer 22

Finally we need the degree of the polynomial.
The degree of a polynomial is the same as the highest degree of all of its terms.
Since the first term is of 4th degree, this is a 4th degree polynomial.

Answer 23

Now we combine the degree with the type of polynomial and we can call this:
a 4th degree trinomial

Answer 24

Ohhhh Thanks man!!!!!!!!! That's the first time the degree system made sense!!!

Answer 25

AWESOME, THIS IS THE FIRST TIME I'VE SMILED WITH POLYNOMIALS IN THE ROOM

Answer 26

Now you know it!
Keep studying and asking questions.
That's how you learn.

Answer 27

You are welcome.

Answer 28

Can I tag you later if I have another question?

Answer 29

Of course. Feel free to ask me questions any time you see me online.
I am getting off soon, though.

Answer 30

Okay :)