SOLUTION: Can you tell me the degree of this polynomial 3^2-2x-7^3+2? Need help. This stuff is new to me.

Question 309477: Can you tell me the degree of this polynomial 3^2-2x-7^3+2? Need help. This stuff is new to me.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
Your equation is:

is equal to 9.
is equal to 343.

This makes your equation equivalent to:

Combine like terms to get:

Your polynomial simplifies to 2 terms.

The sum of the exponents in the first term is equal to 1.
The sum of the exponents in the second term is equal to 0.

The term with the highest sum of exponents determines the degree of the polynomial.

The degree of the polynomial is the sum of the exponents in that term.

The degree of your polynomial is equal to 1.

The fact that the constants had exponents attached to them doesn't count.

It's the exponents of the variables in each term of the polynomial that count.

A constant raised to any power is still a constant.

The rules for what is a polynomial are reasonably simple, but the determination of whether a polynomial fits those rules can get complicated.

It's best to simplify the polynomial as much as possible before deciding.

A polynomial that looks like it violates the rules before simplification may turn out to not violate the rules after simplification.

The rules are:

The exponents of the variables have to be zero or positive only.
The exponents of the variables have to be integer only.
The terms in the expression can be added or subtracted from each other only.
The variables within each term have to be multiplied by each other only.

Some examples:

sqrt(x) = x^(1/2) which is not allowed.
sqrt(x^2) = x which is allowed.
x/5 = (1/5)*x which is allowed.
5/x = 5*(1/x) = 5*x^(-1) which is not allowed.
x*y is allowed.
x/y is not allowed.

Dividing a variable by a constant is allowed.
Dividing a constant by a variable is not.
Dividing a variable by another variable is not.

Your expression didn't really violate any rules but they threw you a curve by showing the constants with exponents.

All you have to remember is that a constant is still a constant regardless of what power it is raised to.

It's the degree of the variable that counts, not the degree of the constant.

The degree of a constant is always equal to 0 after you have simplified the constant as much as possible.
Example;
Any variable name can be used to prove the point since any variable raised to the 0 power is equal to 1.

The degree of a variable without an exponent attached is equal to 1.
Example:

Examples of terms and the degree of the term:

= degree of 5
= degree of 5 because the sum of the exponents is equal to 0 + 5.
= degree of 6 because the sum of the exponents is equal to 0 + 5 + 1.
= degree of 9 because the sum of the exponents is equal to 0 + 3 + 4 + 2.

RELATED QUESTIONS
Can anyone help me with this? Identify the degree of each terms of the polynomial and... (answered by stanbon)

Hi, Can you help me with this math problem? State the degree of the... (answered by vleith)

Can you tell me how to solve this? 2/3 is what percent of 5/6 (answered by checkley71)

f(x)= -x^2+4x-3 f(-3) Can you help me with this problem? this is what i've done.... (answered by checkley77)

I need to add the following polynomial: 5b^3-8b+2b^2 and 3b^2-7b^3+5b. Can someone please (answered by checkley75)

Determine a polynomial function of lowest degree with rational coefficients that has the... (answered by tommyt3rd)

I need to classify this polynomial by degree and by number of terms. I'm able to figure... (answered by Edwin McCravy)

Hi, can you please help me?? 1. I need to factor this problem first: 2x^2+2x+1... (answered by jsmallt9)

What is the answer to this equation: 5x=+10-6x+3=6-2x-2 and can you tell me how you... (answered by drj)