Which type of polynomial is #5x^3-3x^2+x+6#?

1 Answer
May 2, 2016

It is called a cubic, or more specifically a cubic polynomial in one variable #x# with integer coefficients.

Explanation:

The degree of each term is the power of #x#.

  • #5x^3# has degree #3#
  • #-3x^2# has degree #2#
  • #x# has degree #1#
  • #6# has degree #0#

The degree of the polynomial is the maximum degree of its terms.

So in our example, the polynomial is of degree #3#

A polynomial of degree #3# is called a "cubic polynomial" or "cubic" for short.

The names of the first few degrees of polynomial are:

  • #0# - constant
  • #1# - linear
  • #2# - quadratic
  • #3# - cubic
  • #4# - quartic
  • #5# - quintic
  • #6# - sextic (or hexic)
  • #7# - septic (yes - really!) (or heptic)
  • #8# - octic
  • #9# - nonic
  • #10# - decic