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

Mar 22, 2018

See below

Explanation:

A polynomial $n$ degree in standar form is

$p \left(x\right) = {a}_{n} {x}^{n} + {a}_{n - 1} {x}^{n - 1} + \ldots + {a}_{2} {x}^{2} + {a}_{1} x + {a}_{0}$

Which have $n + 1$ terms (from ${a}_{0}$ to ${a}_{n}$)

In particular case of $5 - 3 x$ 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 ${x}^{0} = 1$).

Mar 22, 2018

In standard form: $\textcolor{b l u e}{- 3 x + 5}$
Degree: $\textcolor{b l u e}{1}$
Number of terms: $\textcolor{b l u e}{2}$

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:
$\textcolor{w h i t e}{\text{XXX}} - 3 x + 5$