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?

1 Answer
Patrick H.
Dec 23, 2017

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.

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