Solve -11-66a^2-99a^4

$$- 11 - 66 a ^ { 2 } - 99 a ^ { 4 }$$

Factor

$$-11\left(3a^{2}+1\right)^{2}$$

Solution Steps

Factor out 11.

$$11\left(-1-6a^{2}-9a^{4}\right)$$

Consider -1-6a^{2}-9a^{4}. Find one factor of the form ka^{m}+n, where ka^{m} divides the monomial with the highest power -9a^{4} and n divides the constant factor -1. One such factor is 3a^{2}+1. Factor the polynomial by dividing it by this factor.

$$\left(3a^{2}+1\right)\left(-3a^{2}-1\right)$$

Rewrite the complete factored expression. The following polynomials are not factored since they do not have any rational roots: -3a^{2}-1,3a^{2}+1.

$$11\left(3a^{2}+1\right)\left(-3a^{2}-1\right)$$

Evaluate

$$-11\left(3a^{2}+1\right)^{2}$$