Solve {l}{x^4+23x^2+256}{+23x^2+256}

$$\left. \begin{array} { l } { x ^ { 4 } + 23 x ^ { 2 } + 256 } \\ { + 23 x ^ { 2 } + 256 } \end{array} \right.$$

Evaluate

$$x^{4}+46x^{2}+512$$

Solution Steps

Combine 23x^{2} and 23x^{2} to get 46x^{2}.

$$x^{4}+46x^{2}+256+256$$

Add 256 and 256 to get 512.

$$x^{4}+46x^{2}+512$$

Factor

$$\left(x^{2}-\left(-\sqrt{17}-23\right)\right)\left(x^{2}-\left(\sqrt{17}-23\right)\right)$$