Solve -1/4x^4+4

$$- \frac{ 1 }{ 4 } { x }^{ 4 } +4$$

Factor

$$\frac{\left(x-2\right)\left(x+2\right)\left(-x^{2}-4\right)}{4}$$

Solution Steps

Factor out \frac{1}{4}.

$$\frac{-x^{4}+16}{4}$$

Consider -x^{4}+16. Rewrite -x^{4}+16 as 4^{2}-\left(-x^{2}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

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

Reorder the terms.

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

Consider -x^{2}+4. Rewrite -x^{2}+4 as 2^{2}-x^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(2-x\right)\left(2+x\right)$$

Reorder the terms.

$$\left(-x+2\right)\left(x+2\right)$$

Rewrite the complete factored expression. Polynomial x^{2}+4 is not factored since it does not have any rational roots.

$$\frac{\left(x^{2}+4\right)\left(-x+2\right)\left(x+2\right)}{4}$$

Evaluate

$$-\frac{x^{4}}{4}+4$$