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Answer :
We begin with the polynomial
[tex]$$6x^3 - 8x^4 + 5x + 12x^2 - 9.$$[/tex]
The standard form of a polynomial is one in which the terms are arranged in descending order with respect to the degree (the power of [tex]$x$[/tex]). Here’s how to arrange the polynomial step by step:
1. Identify the term with the highest power. In this polynomial, the term [tex]$-8x^4$[/tex] is the term with the highest power ([tex]$4$[/tex]).
2. The next term is [tex]$6x^3$[/tex], which is of degree [tex]$3$[/tex].
3. Then comes [tex]$12x^2$[/tex], the degree [tex]$2$[/tex] term.
4. Next is [tex]$5x$[/tex], which is the degree [tex]$1$[/tex] term.
5. Lastly, the constant term [tex]$-9$[/tex] is of degree [tex]$0$[/tex].
Arranging the terms in descending powers, we have:
[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]
Among the given choices, this corresponds to option 4.
[tex]$$6x^3 - 8x^4 + 5x + 12x^2 - 9.$$[/tex]
The standard form of a polynomial is one in which the terms are arranged in descending order with respect to the degree (the power of [tex]$x$[/tex]). Here’s how to arrange the polynomial step by step:
1. Identify the term with the highest power. In this polynomial, the term [tex]$-8x^4$[/tex] is the term with the highest power ([tex]$4$[/tex]).
2. The next term is [tex]$6x^3$[/tex], which is of degree [tex]$3$[/tex].
3. Then comes [tex]$12x^2$[/tex], the degree [tex]$2$[/tex] term.
4. Next is [tex]$5x$[/tex], which is the degree [tex]$1$[/tex] term.
5. Lastly, the constant term [tex]$-9$[/tex] is of degree [tex]$0$[/tex].
Arranging the terms in descending powers, we have:
[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]
Among the given choices, this corresponds to option 4.
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