Question

ok last question for today yeah

f(x)=3-6x

a. does this represent a polynomial?
b. What degree?
c. what is the type

Answer 1

a good way to look at this is to say "is the equation continuous and differentiable" if the answers are yes then its a polynomial. the degree is the highest exponent on the variable, and monomials have one term, binomials have two terms, trinomials have three terms, and to keep it simple all others are polynomials

Answer 2

A polynomial is made up of one term or a sum of terms.
A term is a number by itself or a number multiplied by any number of variables.
The degree of a term is the sum of the exponents of all the variables of that term.
The degree of a polynomial is the same as the highest degree of any of its terms.

Look at what you're given in this question and see if it fits the bill.
Is 3 a term?
Is -6x a term?

Answer 3

i am going to say yes to both even though there is a -6

Answer 4

Look at what a term can be:
(a) A number by itself
(b) A number multiplied by any number of variables.
3 is a number, so 3 is a term.
-6x is a number multiplied by one variable, so -6x is a term
So far so good?

Answer 5

yeah, so then the degree is going to 2 right

Answer 6

Not yet.

Answer 7

So far we see we have two terms. Now a polynomial is when you have a single term or a sum of terms.
is 3 - 6x a single term or a sum of terms?

Answer 8

3 - 6x can be thought of as 3 + (-6x)
Is it a sum of terms?

Answer 9

single because 3 can go into both

Answer 10

but it is 2 so it should be sum of terms

Answer 11

nothing is going anywhere. you have a sum of terms. you have two terms, one is 3. the other one is -6x. That's two terms. You add them together, and you get 3 + (-6x) which can be written as 3 - 6x. It's a sum of terms, so it's a polynomial

Answer 12

Now, what about the degree? The degree of a term is the sum of the exponents of all variables in that term.

Answer 13

so that would be 2 then because 3 and 6 right

Answer 14

The term 3 has no variable. Its degree is zero
The term -6x has one variable. Its degree is 1, so the degree of teh term -6x is one.
The degree of a polynomial is the same as the degree of the highest term. Since one term has degree 1 and one term has degree 0, and 1 is higher than zero, the degree of this polynomial is 1.

Answer 15

A polynomial of first degree is called a linear polynomial because its graph is a straight line.