Solve 36-x^12=

$$36 - x ^ { 12 } =$$

Factor

$$\left(-x^{6}-6\right)\left(x^{6}-6\right)$$

Solution Steps

Rewrite 36-x^{12} as 6^{2}-\left(-x^{6}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(6+x^{6}\right)\left(6-x^{6}\right)$$

Reorder the terms. The following polynomials are not factored since they do not have any rational roots: -x^{6}+6,x^{6}+6.

$$\left(x^{6}+6\right)\left(-x^{6}+6\right)$$

Evaluate

$$36-x^{12}$$