How do you name polynomials?

Answer 1

There are 2 ways to name a polynomial: by its degree (the highest power) and by the number of terms it has.

Some of the most common names based on degree are:

constant (meaning there is no variable--5 or 23, for instance; you could also realize that the variable is being raised to the 0 power),

linear (the variable is raised to the first power--3x),

quadratic (x2),

cubic (x3),

quartic (x4), and

quintic (x5).

Keep in mind that these terms could have any coefficients and any number of terms, just be sure you name it based on the highest power (ex: 3x4 + 5x3 - 2x is a quartic polynomial, whereas 3x4 + 5x3 - 2x5 would be a quintic polynomial).

To name a polynomial based on the number of terms, make sure you've simplified it by combining all like terms, then count them up. If the polynomial has:

1 term--monomial (mono- means 1; like a monorail)

2 terms--binomial (bi- means 2; like a bicycle)

3 terms--trinomial (tri- means 3; like a triangle)

4 or more terms--just call it a polynomial, unless your teacher gives you more names (poly- means many; like a polygon).

Keep in mind that these terms will often be used together: 3x4 + 5x3 - 2x is a quartic trinomial. (You may be thinking that I was wrong above where I called this same example a quartic polynomial--that was also correct, since monomial, binomial, and trinomial are all just more specific names for a polynomial)