Question

How do you write a polynomial in standard form, then classify it by degree and number of terms `5-3x`?

Answer 1

See below

Explanation:

A polynomial `n` degree in standar form is

`p(x)=a_nx^n+a_(n-1)x^(n-1)+...+a_2x^2+a_1x+a_0`

Which have `n+1` terms (from `a_0` to `a_n`)

In particular case of `5-3x` is a plynomial of two terms and degree `1`. Coefficientes are `-3` (of the first degree) and `5` independent term (or degree zero term because `x^0=1`).

Answer 2

In standard form: `color(blue)(-3x+5)`
Degree: `color(blue)1`
Number of terms: `color(blue)2`

Explanation:

In standard form, the terms of a polynomial are arranged in decreasing degree.

The degree of a polynomial is the largest degree of any of its terms.

The degree of a term is the sum of the exponents on all variables in the term.

Terms of a polynomial are the sub-components of the polynomial connected by to other components by only addition or subtraction.

As originally given:
`{: ("first term:",color(magenta)(5),color(white)("xx"),"degree: "color(magenta)0" (since "5=5x^color(magenta)0")"), ("second term: ",color(magenta)(-3x),,"degree: "color(magenta)1" since "-3x=-3x^color(magenta)0")") :}`

Arranged in decreasing degrees:
`color(white)("XXX")-3x+5`