Question

How do you write a polynomial in standard form, then classify it by degree and number of terms `12x^3 + 5 - 5x^2 - 6x^2 + 3x^3 + 2 - x`?

Answer 1

Combine like terms to simplify it into a polynomial.

Explanation:

Let's combine like terms first (i.e. Anything with `x^3` can be combined, anything with `x^2` can be combined, etc.):

`12x^3+5-5x^2-6x^2+3x^3+2-x`
(Resort the numbers into standard form, to make it easier to simplify)
`12x^3+3x^3-5x^2-6x^2-x+5+2`
(Combine like terms)
`15x^3-11x^2-x+7`

We now have our simplified polynomial. This can be classified as a 3rd degree polynomial
We classify by number of terms by finding how many individual terms there are. `15x^3`, `11x^2`, `x`, and `7` are all four of our terms, so we have a polynomial (Any polynomial with four or more terms is just called a polynomial.)
We classify by degree by finding the highest exponent on any of the terms. The exponent 3 is the highest term, so this polynomial is a 3rd degree polynomial.