Solve m^4-4m^2-21

$$m ^ { 4 } - 4 m ^ { 2 } - 21$$

Factor

$$\left(m^{2}-7\right)\left(m^{2}+3\right)$$

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 -21. One such factor is m^{2}-7. 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}-7,m^{2}+3.

$$\left(m^{2}-7\right)\left(m^{2}+3\right)$$

Evaluate

$$\left(m^{2}-7\right)\left(m^{2}+3\right)$$