Answer :

We start with the polynomial

[tex]$$9x^3 - 5x^7 + 8x - x^2.$$[/tex]

Our goal is to write the polynomial in standard form, which means arranging the terms in descending order of the exponents of [tex]$x$[/tex]. The steps are as follows:

1. Identify the exponent of [tex]$x$[/tex] in each term:
- The term [tex]$9x^3$[/tex] has exponent 3.
- The term [tex]$-5x^7$[/tex] has exponent 7.
- The term [tex]$8x$[/tex] has exponent 1.
- The term [tex]$-x^2$[/tex] has exponent 2.

2. Rearrange the terms in descending order by the exponent values. The highest exponent is 7, followed by 3, then 2, and finally 1. This gives us:

[tex]$$-5x^7 + 9x^3 - x^2 + 8x.$$[/tex]

Thus, the polynomial in standard form is:

[tex]$$-5x^7 + 9x^3 - x^2 + 8x.$$[/tex]

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Rewritten by : Barada