Solve m^4+6m^2-16

$$m ^ { 4 } + 6 m ^ { 2 } - 16$$

Factor

$$\left(m^{2}-2\right)\left(m^{2}+8\right)$$

Solution Steps

Find one factor of the form m^{k}+n, where m^{k} divides the monomial with the highest power m^{4} and n divides the constant factor -16. One such factor is m^{2}+8. Factor the polynomial by dividing it by this factor. The following polynomials are not factored since they do not have any rational roots: m^{2}-2,m^{2}+8.

$$\left(m^{2}+8\right)\left(m^{2}-2\right)$$

Evaluate

$$\left(m^{2}-2\right)\left(m^{2}+8\right)$$