What is a polynomial that is in standard form?

Question

anonymous · Answer

@tHe_FiZiCx99

opcode · Answer

Post the polynomial?

anonymous · Answer

i dont have one i have to make one thats why i need to know what a polynomial is that is in standard form

opcode · Answer

Oops, sorry I read the question wrong.

What a polynomial is:
A polynomial is an algebraic expression with more than two terms.

Do you know what a binomial is?

anonymous · Answer

its okay and I know what polynomials are (: and binomials are the sum or difference of two terms

opcode · Answer

Great so:
Monomial: $7x$ (A monomial can only have one term.)
Binomial: $7x + 8$ (A binomial can only have two terms.)
Polynomial: $x^2 − 8x + 9$ (A polynomial can have more than two terms.)

anonymous · Answer

Trinomial which would be 8x+9x+5x  right?

opcode · Answer

Tri = Three so yes.

mathstudent55 · Answer

8x+9x+5x is not a good example of a trinomial. 
Since all terms have only the variable x, they are like terms and can be combined together.
8x+9x+5x = 22x

An example of a trinomial is 8x + 9y + 5z

opcode · Answer

Oops I was about to correct my mistake :-P.

anonymous · Answer

Ah okay but i know all of this and my question is still not answered....what is a polynomial that is in standard form /:

opcode · Answer

Standard form of a polynomial is to have the terms with the degrees that are the highest go first:
$$x^6 + 4x^3 + 3x^2 - 7$$

mathstudent55 · Answer

First start with a term.
A term is a number or a number multiplied by one or more variables.
Examples of terms: $2$, $5x$, $6ab$, $-8ab^2$
The degree of a term is the sum of the exponents of all the variables of the term.

mathstudent55 · Answer

A polynomial is a sum of terms.
Standard form of a polynomial is to write the polynomial in descending order of degree of its terms.

anonymous · Answer

Oh okay thank you both I just needed to know it was the highest to lowest/descendng orer of the degree of its terms i can do the rest (:

mathstudent55 · Answer

For example, for the polynomial:

$3x^6 - 4x^7 + 2x^2 + 8 - 6x^3$

standard form is:

$-4x^7 + 3x^6 - 6x^3 + 2x^2 + 8$

where you see the degree of each subsequent term is lower.

mathstudent55 · Answer

You're welcome.