Answer
$R=1$
$x+4$ is not a factor.
Work Step by Step
$f\left( x\right) =4x^{6}-64x^{4}+x^{2}-15=\left( x+4\right) q\left( x\right) +R$
$\Rightarrow f\left( -4\right) =1=R\neq 0$
Since $R\ne0$, $x+4$ is not a factor.
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