Solve -16y^4-16y^2-4

$$- 16 y ^ { 4 } - 16 y ^ { 2 } - 4$$

Factor

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

Solution Steps

Factor out 4.

$$4\left(-4y^{4}-4y^{2}-1\right)$$

Consider -4y^{4}-4y^{2}-1. Find one factor of the form ky^{m}+n, where ky^{m} divides the monomial with the highest power -4y^{4} and n divides the constant factor -1. One such factor is 2y^{2}+1. Factor the polynomial by dividing it by this factor.

$$\left(2y^{2}+1\right)\left(-2y^{2}-1\right)$$

Rewrite the complete factored expression. The following polynomials are not factored since they do not have any rational roots: -2y^{2}-1,2y^{2}+1.

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

Evaluate

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