Question

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

Answer 1

This is a quadratic binomial.

Explanation:

Given:

`x-6x^2`

To write this in standard form, put the terms in descending order of powers of `x` to get:

`-6x^2+x`

The term of highest degree is `2`, so we call this a quadratic polynomial.

Here are the names of polynomials of the first few degrees:

`1` - Linear

`2` - Quadratic

`3` - Cubic

`4` - Quartic

`5` - Quintic

`6` - Sextic or Hextic

`7` - Septic (!) or Heptic

`8` - Octic

`9` - Nonic

`10` - Decic

The given polynomial consists of two terms, so it is called a binomial.

Here are the names given to expressions consisting of `n` terms for the first few values of `n`:

`1` - Monomial

`2` - Binomial

`3` - Trinomial

`4` - Quadrinomial