Question

How do you write a polynomial in standard form, then classify it by degree and number of terms `4x^2 + x^5 - 12 + 6x`?

Answer 1

Standard form: `color(blue)(x^5+4x^2+6x-12)`
Degree: `color(blue)(5)`
Number of terms: `color(blue)(4)`

Explanation:

Definition: The degree of a polynomial is largest degree of any term in the polynomial.

Definition: The degree of a term in a polynomial is the exponent of the variable in the term (if there is more than one variable, the degree is the sum of the exponents of the variables in that term).

In standard form the terms of a polynomial are ordered in decreasing degree.