Solve t^4+3t^2-70

$$t ^ { 4 } + 3 t ^ { 2 } - 70$$

Factor

$$\left(t^{2}-7\right)\left(t^{2}+10\right)$$

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 -70. One such factor is t^{2}+10. 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}-7,t^{2}+10.

$$\left(t^{2}+10\right)\left(t^{2}-7\right)$$

Evaluate

$$\left(t^{2}-7\right)\left(t^{2}+10\right)$$