Urdorfs4u

2022-02-05

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

powrotnik5ld

Beginner2022-02-06Added 12 answers

Explanation:

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

$12{x}^{3}+5-5{x}^{2}-6{x}^{2}+3{x}^{3}+2-x$

(Resort the numbers into standard form, to make it easier to simplify)

$12{x}^{3}+3{x}^{3}-5{x}^{2}-6{x}^{2}-x+5+2$

(Combine like terms)

$15{x}^{3}-11{x}^{2}-x+7$

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.

$15{x}^{3},11{x}^{2},x$ , amd 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.

Let's combine like terms first (i.e. Anything with

(Resort the numbers into standard form, to make it easier to simplify)

(Combine like terms)

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.

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.