Solve 7m^4-54m^2-16

$$7 m ^ { 4 } - 54 m ^ { 2 } - 16$$

Factor

$$\left(m^{2}-8\right)\left(7m^{2}+2\right)$$

Solution Steps

Find one factor of the form km^{n}+p, where km^{n} divides the monomial with the highest power 7m^{4} and p divides the constant factor -16. One such factor is 7m^{2}+2. 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}-8,7m^{2}+2.

$$\left(7m^{2}+2\right)\left(m^{2}-8\right)$$

Evaluate

$$\left(m^{2}-8\right)\left(7m^{2}+2\right)$$