Solve 20a^4+a^2-1

$$20 a ^ { 4 } + a ^ { 2 } - 1$$

Factor

$$\left(5a^{2}-1\right)\left(4a^{2}+1\right)$$

Solution Steps

Find one factor of the form ka^{m}+n, where ka^{m} divides the monomial with the highest power 20a^{4} and n divides the constant factor -1. One such factor is 4a^{2}+1. Factor the polynomial by dividing it by this factor. The following polynomials are not factored since they do not have any rational roots: 5a^{2}-1,4a^{2}+1.

$$\left(4a^{2}+1\right)\left(5a^{2}-1\right)$$

Evaluate

$$20a^{4}+a^{2}-1$$