Factorise:

$4 x^{4}+7 x^{2}-2=4 x^{4}+8 x^{2}-x^{2}-2$

$=4 x^{2}\left(x^{2}+2\right)-1\left(x^{2}+2\right)$

$=\left(4 x^{2}-1\right)\left(x^{2}+2\right)$

Hence, factorisation of $4 x^{4}+7 x^{2}-2$ is $\left(4 x^{2}-1\right)\left(x^{2}+2\right)$.