Solve r^4+6r^2+5

$$r ^ { 4 } + 6 r ^ { 2 } + 5$$

Factor

$$\left(r^{2}+1\right)\left(r^{2}+5\right)$$

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 5. One such factor is r^{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: r^{2}+1,r^{2}+5.

$$\left(r^{2}+5\right)\left(r^{2}+1\right)$$

Evaluate

$$\left(r^{2}+1\right)\left(r^{2}+5\right)$$