Answer :
To write the polynomial in standard form, we need to arrange the terms in order of descending powers of [tex]$x$[/tex]. The polynomial given is
[tex]$$
x^3 - 7x + 7x^5 - 19 + x^2.
$$[/tex]
Follow these steps:
1. Identify the terms and their degrees:
- [tex]$7x^5$[/tex] is of degree 5.
- [tex]$x^3$[/tex] is of degree 3.
- [tex]$x^2$[/tex] is of degree 2.
- [tex]$-7x$[/tex] is of degree 1.
- [tex]$-19$[/tex] is the constant term (degree 0).
2. Reorder the terms from the highest degree to the lowest degree:
- Start with [tex]$7x^5$[/tex].
- Next, include [tex]$x^3$[/tex].
- Then, include [tex]$x^2$[/tex].
- Follow with [tex]$-7x$[/tex].
- Finally, write the constant [tex]$-19$[/tex].
Thus, the polynomial in standard form is
[tex]$$
7x^5 + x^3 + x^2 - 7x - 19.
$$[/tex]
[tex]$$
x^3 - 7x + 7x^5 - 19 + x^2.
$$[/tex]
Follow these steps:
1. Identify the terms and their degrees:
- [tex]$7x^5$[/tex] is of degree 5.
- [tex]$x^3$[/tex] is of degree 3.
- [tex]$x^2$[/tex] is of degree 2.
- [tex]$-7x$[/tex] is of degree 1.
- [tex]$-19$[/tex] is the constant term (degree 0).
2. Reorder the terms from the highest degree to the lowest degree:
- Start with [tex]$7x^5$[/tex].
- Next, include [tex]$x^3$[/tex].
- Then, include [tex]$x^2$[/tex].
- Follow with [tex]$-7x$[/tex].
- Finally, write the constant [tex]$-19$[/tex].
Thus, the polynomial in standard form is
[tex]$$
7x^5 + x^3 + x^2 - 7x - 19.
$$[/tex]
