If $x+1$ is a factor of $ax^4 + bx^2 + c,$ what is the value of $a + b + c?$

Question

The same question was posed here Find the value of a+b+c but I cannot make sense of the answer.

My long division must be incorrect as I ended up with $a+b+c$ which is definitely wrong. I added $0$ to represent $x^3$ and $x^1$ terms.

I know the remainder should be zero if $x+1$ is a factor.

I am not putting two and two together.

Answer 1

$x = -1$ is a root of polynomial
put $x = -1$ in $a x^4 + b x^2 + c$
$a + b + c = 0$