Answer :
To write the polynomial
$$3x^3 + 9x^7 - x + 4x^{12}$$
in descending order, we first identify the exponent for each term:
1. The term $3x^3$ has an exponent of $3$.
2. The term $9x^7$ has an exponent of $7$.
3. The term $-x$ can be written as $-1x^1$, with an exponent of $1$.
4. The term $4x^{12}$ has an exponent of $12$.
Next, we order the terms from the highest exponent to the lowest:
- The highest exponent is $12$: this gives $4x^{12}$.
- The next highest exponent is $7$: this gives $9x^7$.
- Then exponent $3$: this gives $3x^3$.
- Finally, the lowest exponent is $1$: this gives $-x$.
Thus, the polynomial written in descending order is:
$$4x^{12} + 9x^7 + 3x^3 - x.$$
Comparing with the given options, the correct answer is option D.
$$3x^3 + 9x^7 - x + 4x^{12}$$
in descending order, we first identify the exponent for each term:
1. The term $3x^3$ has an exponent of $3$.
2. The term $9x^7$ has an exponent of $7$.
3. The term $-x$ can be written as $-1x^1$, with an exponent of $1$.
4. The term $4x^{12}$ has an exponent of $12$.
Next, we order the terms from the highest exponent to the lowest:
- The highest exponent is $12$: this gives $4x^{12}$.
- The next highest exponent is $7$: this gives $9x^7$.
- Then exponent $3$: this gives $3x^3$.
- Finally, the lowest exponent is $1$: this gives $-x$.
Thus, the polynomial written in descending order is:
$$4x^{12} + 9x^7 + 3x^3 - x.$$
Comparing with the given options, the correct answer is option D.
