Answer :
We start with the polynomial
[tex]$$4x^2 - x + 8x^6 + 3 + 2x^{10}.$$[/tex]
The first step is to identify each term along with its corresponding power of [tex]$x$[/tex]:
- The term [tex]$2x^{10}$[/tex] has exponent 10.
- The term [tex]$8x^6$[/tex] has exponent 6.
- The term [tex]$4x^2$[/tex] has exponent 2.
- The term [tex]$-x$[/tex] has exponent 1.
- The constant [tex]$3$[/tex] can be considered as [tex]$3x^0$[/tex], with exponent 0.
Next, we rewrite the polynomial by arranging the terms in descending order of their exponents:
1. The highest exponent is 10, so the first term is [tex]$2x^{10}$[/tex].
2. Next is exponent 6, giving the term [tex]$8x^6$[/tex].
3. Then exponent 2 gives [tex]$4x^2$[/tex].
4. Followed by exponent 1, which gives [tex]$-x$[/tex].
5. Finally, exponent 0 gives the term [tex]$3$[/tex].
Thus, the polynomial in descending order is
[tex]$$2x^{10} + 8x^6 + 4x^2 - x + 3.$$[/tex]
Comparing this with the provided answer choices, we see that the correct choice is:
[tex]$$2x^{10}+8x^6+4x^2-x+3.$$[/tex]
[tex]$$4x^2 - x + 8x^6 + 3 + 2x^{10}.$$[/tex]
The first step is to identify each term along with its corresponding power of [tex]$x$[/tex]:
- The term [tex]$2x^{10}$[/tex] has exponent 10.
- The term [tex]$8x^6$[/tex] has exponent 6.
- The term [tex]$4x^2$[/tex] has exponent 2.
- The term [tex]$-x$[/tex] has exponent 1.
- The constant [tex]$3$[/tex] can be considered as [tex]$3x^0$[/tex], with exponent 0.
Next, we rewrite the polynomial by arranging the terms in descending order of their exponents:
1. The highest exponent is 10, so the first term is [tex]$2x^{10}$[/tex].
2. Next is exponent 6, giving the term [tex]$8x^6$[/tex].
3. Then exponent 2 gives [tex]$4x^2$[/tex].
4. Followed by exponent 1, which gives [tex]$-x$[/tex].
5. Finally, exponent 0 gives the term [tex]$3$[/tex].
Thus, the polynomial in descending order is
[tex]$$2x^{10} + 8x^6 + 4x^2 - x + 3.$$[/tex]
Comparing this with the provided answer choices, we see that the correct choice is:
[tex]$$2x^{10}+8x^6+4x^2-x+3.$$[/tex]
