Answer :
To write the polynomial in standard form, we need to arrange its terms in descending order by the exponent of [tex]\( x \)[/tex]. Follow these steps:
1. Start with the original polynomial:
[tex]$$
6x^3 - 8x^4 + 5x + 12x^2 - 9.
$$[/tex]
2. Identify each term with its corresponding exponent:
- The term with [tex]\( x^4 \)[/tex] is [tex]\( -8x^4 \)[/tex].
- The term with [tex]\( x^3 \)[/tex] is [tex]\( 6x^3 \)[/tex].
- The term with [tex]\( x^2 \)[/tex] is [tex]\( 12x^2 \)[/tex].
- The term with [tex]\( x^1 \)[/tex] is [tex]\( 5x \)[/tex].
- The constant term (with [tex]\( x^0 \)[/tex]) is [tex]\( -9 \)[/tex].
3. Arrange these terms in descending order of exponent (from highest to lowest):
[tex]$$
-8x^4 + 6x^3 + 12x^2 + 5x - 9.
$$[/tex]
Thus, the polynomial in standard form is:
[tex]$$
-8x^4 + 6x^3 + 12x^2 + 5x - 9.
$$[/tex]
This corresponds to option 4.
1. Start with the original polynomial:
[tex]$$
6x^3 - 8x^4 + 5x + 12x^2 - 9.
$$[/tex]
2. Identify each term with its corresponding exponent:
- The term with [tex]\( x^4 \)[/tex] is [tex]\( -8x^4 \)[/tex].
- The term with [tex]\( x^3 \)[/tex] is [tex]\( 6x^3 \)[/tex].
- The term with [tex]\( x^2 \)[/tex] is [tex]\( 12x^2 \)[/tex].
- The term with [tex]\( x^1 \)[/tex] is [tex]\( 5x \)[/tex].
- The constant term (with [tex]\( x^0 \)[/tex]) is [tex]\( -9 \)[/tex].
3. Arrange these terms in descending order of exponent (from highest to lowest):
[tex]$$
-8x^4 + 6x^3 + 12x^2 + 5x - 9.
$$[/tex]
Thus, the polynomial in standard form is:
[tex]$$
-8x^4 + 6x^3 + 12x^2 + 5x - 9.
$$[/tex]
This corresponds to option 4.
