<s>[INST] Find the value of a+b+c If $x+1$ is a factor of $ax^4 + bx^2 + c$, find the value of $a + b + c$?
I know that it is equal to zero, but I have to know How to do it.
 [/INST] As a shortcut for the long division, note that if $x+1$ is a factor of $ax^4+bx^2+c=0$, then $x-1$ is also a factor. Divide $ax^4+bx^2+c$ by $(x+1)(x-1)=x^2-1$ to get the remainder $a+b+c$, which must be equal to $0$.
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