what does in the standard form of a polynomial means ? explain

Question

anonymous · Answer

If you googled it, you may find the answer. The answer I believe is that the standard form of a polynomial means the terms are arranged from highest to lowest. It makes sense that many questions with polynomials are grouped together.

An example would be

$$x^{3}+x^{2} - 1$$

unklerhaukus · Answer

$$\text{The standard form of an $n$-th order polynomial}$$ $$a_1x^n+a_2x^{n-1}+a_{3}x^{n-2}+\dots+a_{n-1}x^2+a_{n}x+a_{n+1}$$
where the $a_1...a_n$ terms are the co-efficients 
 $a_1$ is nonzero (or else it wolden't be $n$-th order)
and $a_{n+1}$ is the constant term.

Note that there can be a most  $n+1$ terms

Also note that the powers of $x$ are in descending order (left to right)

There will be less terms if any of  $a_{2}\dots a_{n+1}$ are equal to zero

unklerhaukus · Answer

for example a particular 4rd order polynomial might be 
$$x^4+4+x+6x^3$$
to convert this to standard form we need to arrange the terms in decreasing order of the powers of $x$.
(it might help to show the powers of $x$ more explicitly )
$$x^4+4x^0+x^1+6x^3$$
now rearranging the terms
$$x^4+6x^3+x^1+4x^0$$
we arrive at
$$x^4+6x^3+x+4$$
This is in standard from 

the coefficient of $x^4$ is $1$
the coefficient of $x^3$ is $6$
the coefficient of $x^2$ is $0$
the coefficient of $x$ is $1$
the constant term  is $4$