Question

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`?

Answer 1

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).

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

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