Solve x^4-x^2-20=

$$x ^ { 4 } - x ^ { 2 } - 20 =$$

Factor

$$\left(x^{2}-5\right)\left(x^{2}+4\right)$$

Solution Steps

Find one factor of the form x^{k}+m, where x^{k} divides the monomial with the highest power x^{4} and m divides the constant factor -20. One such factor is x^{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: x^{2}-5,x^{2}+4.

$$\left(x^{2}-5\right)\left(x^{2}+4\right)$$

Evaluate

$$\left(x^{2}-5\right)\left(x^{2}+4\right)$$