Factor
\left(z^{2}-2\right)\left(z^{2}+3\right)
Evaluate
z^{4}+z^{2}-6
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\left(z^{2}+3\right)\left(z^{2}-2\right)
Find one factor of the form z^{k}+m, where z^{k} divides the monomial with the highest power z^{4} and m divides the constant factor -6. One such factor is z^{2}+3. Factor the polynomial by dividing it by this factor. The following polynomials are not factored since they do not have any rational roots: z^{2}-2,z^{2}+3.
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