If $-4<x<8$then the value of $x^2-4x-32$ is

$f\left(x\right)=x^2-4x-32=x^2-8x+4x-32$

$=x(x-8)+4(x-8)$

$=(x-8)(x+4)$

$-4<x<8\Rightarrow a\&EXP$ will have opposite sign

$x<-4\left(or\right)x>8\Rightarrow a\&EXP$ same sign

$-4<x<8\to a>0Exp<0(-ve)$