Solve 125-t^6quad1

$$125 - t ^ { 6 } \quad 1$$

Evaluate

$$125-t^{6}$$

Solution Steps

Multiply -1 and 1 to get -1.

$$125-t^{6}$$

Factor

$$\left(t^{2}-5\right)\left(-t^{4}-5t^{2}-25\right)$$

Solution Steps

Find one factor of the form kt^{m}+n, where kt^{m} divides the monomial with the highest power -t^{6} and n divides the constant factor 125. One such factor is t^{2}-5. Factor the polynomial by dividing it by this factor. The following polynomials are not factored since they do not have any rational roots: -t^{4}-5t^{2}-25,t^{2}-5.

$$\left(t^{2}-5\right)\left(-t^{4}-5t^{2}-25\right)$$