Solve a^4-a^2-56

$${ a }^{ 4 } - { a }^{ 2 } -56$$

Factor

$$\left(a^{2}-8\right)\left(a^{2}+7\right)$$

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 -56. One such factor is a^{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: a^{2}-8,a^{2}+7.

$$\left(a^{2}-8\right)\left(a^{2}+7\right)$$

Evaluate

$$\left(a^{2}-8\right)\left(a^{2}+7\right)$$