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

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.

Do you have a similar question?