Question 83530: I NEED HELP ON POLYNOMIALS. FOR FINALS WE NEED TO KNOW WHAT IS THE DEGREE AND NAME OF IT. MY FIRST PROBLEM SAYS: 5X^2 - 3X^2. I NEED YOU TO HELP ME FIGURE OUT THE DEGREE, THE NAME OF THE DEGREE, AND THE NAME BY TERM.
Answer by praseenakos@yahoo.com(507)   (Show Source):
You can put this solution on YOUR website! A polynomial is an algebraic expression that is a sum of terms, where each term contains only variables with whole number exponents and integer coefficients.
Example: The following expressions are all considered polynomials:
 - 4x + 7
+ 2x – 7
x
The following are NOT polynomials:
 , 
A polynomial can have any number of terms (“poly” means “many”). We have special names for polynomials that have one, two, or three terms:
A monomial has one term (“mono” means “one”). The following are monomials:
x,  ,  etc.
A binomial has two terms:
x + 1,  – 3x
A trinomial has three terms:
 – 3x ,  – 4x + 1
The degree of an individual term in a polynomial is the sum of powers of all the variables in that term.
Examples:
 here...Degree = 3
Degree = 4
x ... degree = 1
 Degree = 7 (because 2 + 5 = 7)
37 here Degree = 0, because here you dont have a vairable
Remember that degree of a constat term is always zero.
The degree of the entire polynomial is the degree of the highest-degree term that it contains, so
 + 2x – 7 is a second-degree trinomial,
and is a fourth-degree binomial.
Now come back to your question...it is...
5X^2 - 3X^2. I NEED YOU TO HELP ME FIGURE OUT THE DEGREE, THE NAME OF THE DEGREE, AND THE NAME BY TERM.
In this question you have two terms...they are 5x^2 and 3x^2
Degree of both the terms is 2.
So this is a second degree polynomial.
But here you can simplyfy the given expression(since both the terms are of same degree) as follow.....
 = 
Here we got a single term.....so we can say that the given polynomial is a second degree monomial(since there is only one term)
Hope you found the explanation useful.
Regards.
Praseena.
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