Solve t^4-4t^2-32

$$t ^ { 4 } - 4 t ^ { 2 } - 32$$

Factor

$$\left(t^{2}-8\right)\left(t^{2}+4\right)$$

Solution Steps

Find one factor of the form t^{k}+m, where t^{k} divides the monomial with the highest power t^{4} and m divides the constant factor -32. One such factor is t^{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: t^{2}-8,t^{2}+4.

$$\left(t^{2}-8\right)\left(t^{2}+4\right)$$

Evaluate

$$\left(t^{2}-8\right)\left(t^{2}+4\right)$$