Answer
$$
0=0+0x+0x^2+0x^3+0x^4+0x^5+0x^6+0x^7+0x^8.
$$
$$-u=-a_0-a_1x-a_2x^2-a_3x^3-a_4x^4-a_5x^5-a_6x^6-a_7x^7-a_8x^8.$$
Work Step by Step
The zero vector of the vector space $P_8$ is given by
$$
0=0+0x+0x^2+0x^3+0x^4+0x^5+0x^6+0x^7+0x^8.
$$
Let $u$ be an vector in $P_8$ such that
$$u=a_0+a_1x+a_2x^2+a_3x^3+a_4x^4+a_5x^5+a_6x^6+a_7x^7+a_8x^8.$$
Now, the additive inverse of $u$ is given by
$$-u=-a_0-a_1x-a_2x^2-a_3x^3-a_4x^4-a_5x^5-a_6x^6-a_7x^7-a_8x^8.$$
