Solve v^4+4v^2-21

$$v ^ { 4 } + 4 v ^ { 2 } - 21$$

Factor

$$\left(v^{2}-3\right)\left(v^{2}+7\right)$$

Solution Steps

Find one factor of the form v^{k}+m, where v^{k} divides the monomial with the highest power v^{4} and m divides the constant factor -21. One such factor is v^{2}+7. Factor the polynomial by dividing it by this factor. The following polynomials are not factored since they do not have any rational roots: v^{2}-3,v^{2}+7.

$$\left(v^{2}+7\right)\left(v^{2}-3\right)$$

Evaluate

$$\left(v^{2}-3\right)\left(v^{2}+7\right)$$