Question 83530
 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:



{{{x^2}}} - 4x + 7 



{{{x^2}}} + 2x – 7



{{{x^4 – 7x^3}}}

x



The following are NOT polynomials:

{{{1/x}}} ,   {{{ sqrt(x^3 -4)}}}

 

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,   {{{3x^4}}}  ,    {{{2x^3}}} etc.

A binomial has two terms:

x + 1,   {{{5x^2 }}} – 3x


A trinomial has three terms:

{{{x^4 + 2x^3 }}} – 3x       ,   {{{2x^2}}} – 4x + 1


The degree of an individual term in a polynomial is the sum of powers of all the variables in that term. 




Examples: 

{{{ 2x^ 3 }}}  here...Degree = 3



{{{3x^4}}}  Degree = 4

x ... degree = 1



{{{3x^2y^5}}} 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

{{{x^2 }}} + 2x – 7 is a second-degree trinomial, 


and {{{x^4 – 7x^3}}}  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.....


{{{5x^2 - 3x^2 }}} = {{{ 2x^2 }}}


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.