How do you write a polynomial in standard form, then classify it by degree and number of terms #2x^2 + 3x^3 + 4x^4 + 5x^5#?

1 Answer
Sep 8, 2017

standard form: #5x^5+4x^4+3x^3+2x^2#
degree: 5
number of terms: 4

Explanation:

A polynomial in standard form has the order of it's terms in decreasing degree, where the degree of a term is the (sum of) the exponent(s) of its variables.

For example:
#color(white)("XXX")23p^8# has degree #8#
and
#color(white)("XXX")7r^2t^3# has degree #2+3=5#

In this case, we have the terms:
#color(white)("XXX")2x^2# has degree #2#
#color(white)("XXX")3x^3# has degree #3#
#color(white)("XXX")4x^4# has degree #4#
#color(white)("XXX")5x^5# has degree #5#
placing them in descending order requires that #5x^5# be the first term and #2x^2# be the last term (with the other 2 terms in the obvious sequence).

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The degree of a polynomial (as opposed to the degree of a single term) is the largest value of any of its terms' degrees.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

A term is an element of a polynomial separated from other elements by either addition or subtraction.