Solve r^4+6r^2-16

$$r ^ { 4 } + 6 r ^ { 2 } - 16$$

Factor

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

Solution Steps

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

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

Evaluate

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