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------------------------------------------------ Write [tex]$7x^5 + x^3 + x^2 - 7x - 19$[/tex] in standard form.

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]