Math CentralQuandaries & Queries


Question from betty, a student:

Write in standard form and identify each polynomial by its degree and number of terms. How do you do this?

1. -4 + 3x ˆ2x2
*2x2 ˆ 4 + 3x; quadratic trinomial
*2x2 + 3x ˆ 4; quadratic binomial
*-2x2 + 3x ˆ 4; quadratic trinomial
*-2x2 + 3x ˆ 4; quadratic binomial

Hi Betty,

The terms trinomial, binomial and monomial refer to the number of unlike terms. "tri" indicates 3, "bi" indicates 2 and "mono" indicates 1. For example

$4x^2 + 3x -2$ is a trinomial
$5x - 2x^3$ is a binomial and
$4 - 2x^2 + 5x^4$ is a trinomial.

However $3x - 5x^2 + x$ has three terms but when you collect like terms the expression becomes $4x - 5x^2$ so it is a binomial.

The terms linear, quadratic, cubic, quartic and so on indicate the highest power of the variable. So for my three examples

$4x^2 + 3x -2$ is a quadratic
$5x - 2x^3$ is a cubic and
$4 - 2x^2 + 5x^4$ is a quartic.

Write back if you need more assistance.


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