Answer :
We start with the polynomial
[tex]$$3x^3 + 9x^7 - x + 4x^{12}.$$[/tex]
To write it in descending order, we need to arrange the terms from the highest exponent to the lowest exponent. First, determine the exponents of each term:
- The term [tex]$3x^3$[/tex] has an exponent of [tex]$3$[/tex].
- The term [tex]$9x^7$[/tex] has an exponent of [tex]$7$[/tex].
- The term [tex]$-x$[/tex] has an exponent of [tex]$1$[/tex] (since [tex]$x = x^1$[/tex]).
- The term [tex]$4x^{12}$[/tex] has an exponent of [tex]$12$[/tex].
Now, list the exponents in descending order:
[tex]$$12, \ 7, \ 3, \ 1.$$[/tex]
Next, match these exponents with their corresponding terms:
- Exponent [tex]$12$[/tex]: The term is [tex]$4x^{12}$[/tex].
- Exponent [tex]$7$[/tex]: The term is [tex]$9x^7$[/tex].
- Exponent [tex]$3$[/tex]: The term is [tex]$3x^3$[/tex].
- Exponent [tex]$1$[/tex]: The term is [tex]$-x$[/tex].
Thus, the polynomial in descending order becomes:
[tex]$$4x^{12} + 9x^7 + 3x^3 - x.$$[/tex]
Looking at the multiple-choice options, this corresponds to option C.
[tex]$$3x^3 + 9x^7 - x + 4x^{12}.$$[/tex]
To write it in descending order, we need to arrange the terms from the highest exponent to the lowest exponent. First, determine the exponents of each term:
- The term [tex]$3x^3$[/tex] has an exponent of [tex]$3$[/tex].
- The term [tex]$9x^7$[/tex] has an exponent of [tex]$7$[/tex].
- The term [tex]$-x$[/tex] has an exponent of [tex]$1$[/tex] (since [tex]$x = x^1$[/tex]).
- The term [tex]$4x^{12}$[/tex] has an exponent of [tex]$12$[/tex].
Now, list the exponents in descending order:
[tex]$$12, \ 7, \ 3, \ 1.$$[/tex]
Next, match these exponents with their corresponding terms:
- Exponent [tex]$12$[/tex]: The term is [tex]$4x^{12}$[/tex].
- Exponent [tex]$7$[/tex]: The term is [tex]$9x^7$[/tex].
- Exponent [tex]$3$[/tex]: The term is [tex]$3x^3$[/tex].
- Exponent [tex]$1$[/tex]: The term is [tex]$-x$[/tex].
Thus, the polynomial in descending order becomes:
[tex]$$4x^{12} + 9x^7 + 3x^3 - x.$$[/tex]
Looking at the multiple-choice options, this corresponds to option C.
