Question 724439: For the following polynominal (a) list the degree of each term (b) determine the leading coeficient (c) determine the degree of the polynominal. 2a^5-8+6a^7 (a) the degree of the first term is? the degree of the second term is? the degree of the third term is? (b) the leading term of the polynominal is? the leading coefficient of the polynominal is? (c) the degree of the polynominal is?
I have no idea what to do with this please help me figure it out? Thank you in advance.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! You only list one polynomial, but I guess you just want to see how to do the work through one example.
The expression  is a polynomial.
Polynomials are made of terms added together.
In this case,  ,  and  are the terms of your polynomial.
Each term has a number, called the coefficient, and may have one or more variables, with or without exponents.
Your polynomial has only one variable,  .
DEGREE:
Each term has a degree, which is the sum of the exponents on the variables. Of course, if there is only one variable, there is just one exponent per term, and you do not need to add.
The degree of term is  ,
the degree of is  , and
the degree of is  .
The reason I say the degree of is zero is that  ,
so  .
The degree of the polynomial is the degree of the term of highest degree.
So the degree of your polynomial is .
FIRST TERM:
Polynomials are written starting with the term of highest degree, continuing with the term of next highest degree, and so on. Even very disorganized people, immediately reorganize terms that way when given a jumbled polynomial.
However, I am guessing that if you are asked for the degree of the first term in what's expected is the degree of , the first term in the polynomial as given to you, before you had a chance to re-arrange the terms.
The same would go for "second term" and "third term."
LEADING TERM and LEADING COEFFICIENT:
As polynomials must be written in order of decreasing degree as soon as possible, the leading term is the term of highest degree. And the leading coefficient is the coefficient of the leading term, always written first, in front of the varaiable, leading the whole parade of terms.
So your leading term is and your leading coefficient is 
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