To write the polynomial \( 4x^2 - x + 8x^6 + 3 + 2x^{10} \) in descending order, we need to rearrange the terms so that they are ordered from the highest degree of \( x \) to the lowest.
The terms in the polynomial are:
- \( 2x^{10} \) (degree 10)
- \( 8x^6 \) (degree 6)
- \( 4x^2 \) (degree 2)
- \( -x \) (degree 1)
- \( 3 \) (degree 0)
Now, we can write the polynomial in descending order:
\[ 2x^{10} + 8x^6 + 4x^2 - x + 3 \]
So, the polynomial in descending order is: \[ 2x^{10} + 8x^6 + 4x^2 - x + 3 \]