Answer :
We start with the polynomial
[tex]$$6x^3 - 8x^4 + 5x + 12x^2 - 9.$$[/tex]
The goal is to rewrite this in standard form, which means arranging the terms from the highest-degree term to the lowest-degree term. Follow these steps:
1. Identify the degree of each term:
- The term [tex]$-8x^4$[/tex] has degree 4.
- The term [tex]$6x^3$[/tex] has degree 3.
- The term [tex]$12x^2$[/tex] has degree 2.
- The term [tex]$5x$[/tex] has degree 1.
- The constant [tex]$-9$[/tex] has degree 0.
2. Reorder the terms in descending order (from the highest exponent to the lowest):
[tex]$$-8x^4 + 6x^3 + 12x^2 + 5x - 9.$$[/tex]
This is the polynomial written in standard form.
Thus, the final answer is:
[tex]$$-8x^4 + 6x^3 + 12x^2 + 5x - 9.$$[/tex]
[tex]$$6x^3 - 8x^4 + 5x + 12x^2 - 9.$$[/tex]
The goal is to rewrite this in standard form, which means arranging the terms from the highest-degree term to the lowest-degree term. Follow these steps:
1. Identify the degree of each term:
- The term [tex]$-8x^4$[/tex] has degree 4.
- The term [tex]$6x^3$[/tex] has degree 3.
- The term [tex]$12x^2$[/tex] has degree 2.
- The term [tex]$5x$[/tex] has degree 1.
- The constant [tex]$-9$[/tex] has degree 0.
2. Reorder the terms in descending order (from the highest exponent to the lowest):
[tex]$$-8x^4 + 6x^3 + 12x^2 + 5x - 9.$$[/tex]
This is the polynomial written in standard form.
Thus, the final answer is:
[tex]$$-8x^4 + 6x^3 + 12x^2 + 5x - 9.$$[/tex]
