Solve 4t^4+5t^2-6

$$4 t ^ { 4 } + 5 t ^ { 2 } - 6$$

Factor

$$\left(4t^{2}-3\right)\left(t^{2}+2\right)$$

Solution Steps

Find one factor of the form kt^{m}+n, where kt^{m} divides the monomial with the highest power 4t^{4} and n divides the constant factor -6. One such factor is 4t^{2}-3. Factor the polynomial by dividing it by this factor. The following polynomials are not factored since they do not have any rational roots: 4t^{2}-3,t^{2}+2.

$$\left(4t^{2}-3\right)\left(t^{2}+2\right)$$

Evaluate

$$\left(4t^{2}-3\right)\left(t^{2}+2\right)$$