<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] Let $p(x)=ax^4+bx^2+c$.  We are given $p(x)=(x+1)q(x)$ for $q(x)$ some cubic polynomial.  Now evaluate it at $x=-1$ and we get $p(-1)=a(-1)^4+b(-1)^2+c=a+b+c=0\cdot q(x)=0$ so $a+b+c=0$
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