When is the inequality $x^4<8x^2+9$ satisfied?

Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

The inequality \[x^4<8x^2+9\] is satisfied precisely when \[\text{(a)}-3<x<3 \quad \text{(b)} \quad 0<x<4 \quad \text{(c)} \quad 1<x<3 \quad \text{(d)}-1<x<9 \quad \text{(e)}-3<x<-1.\]

Could we take all of the terms to one side, and then factorise?