Solve a^4-a^2-20

$$a ^ { 4 } - a ^ { 2 } - 20$$

Factor

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

Solution Steps

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

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

Evaluate

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