Question

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

Answer 1

Standard form: `2x^2+x`
Degree: quadratic
Number of terms: binomial

Explanation:

To write a polynomial in standard form, you write starting with the term with the highest degree, or exponent (in this case, the `x^2` term), and then in decreasing order. Since the `x^2` term is the term with the highest degree:
`2x^2+x`

To classify a polynomial by degree, you look at the highest exponent, or degree. Since 2 is the highest exponent (`2x^2`), it is a quadratic. Here are the first few:
Highest Exponent:
`1`- linear
`2`- quadratic
`3`- cubic
`4`- quartic
`5`- quintic

To classify a polynomial by the number of terms, count how many terms are in the polynomial: In this polynomial, there are two terms, `2x^2` and `x`. So, this is a binomial.

1 term- monomial
2 terms- binomial
3 terms- trinomial
4+ terms- polynomial