<s>[INST] How to factor $x^4-7x^2-18$ I am not sure how I would factor this. The $x^4$ and $x^2$ are really throwing me off. Can someone explain how I would factor this?
 [/INST] Solution 1.
\begin{eqnarray*}
x^4-7x^2-18&=&(x^4+2x^2)-(9x^2+18)\\
&=&x^2(x^2+2)-9(x^2+2)\\
&=&(x^2+2)(x^2-9)\\
&=&(x^2+2)(x-3)(x+3)
\end{eqnarray*}
Solution 2.
\begin{eqnarray*}
x^4-7x^2-18&=&(x^4-9x^2)+(2x^2-18)\\
&=&x^2(x^2-9)+2(x^2-9)\\
&=&(x^2-9)(x^2+2)\\
&=&(x-3)(x+3)(x^2+2)
\end{eqnarray*}
Solution 3.
\begin{eqnarray*}
x^4-7x^2-18&=&(x^4-81)-(7x^2-63)\\
&=&(x^2+9)(x^2-9)-7(x^2-9)\\
&=&(x^2-9)(x^2+9-7)\\
&=&(x-3)(x+3)(x^2+2)
\end{eqnarray*}
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