Factoring Challenge: Solve the Quadratic x²-6 as a Binomial Product

To solve the problem, we need to express $x^2 - 6$ in the form of $(x-a)\cdot(x+a)$ because this represents the difference of squares, which is expressed as $(a-b)(a+b) = a^2 - b^2$.

We are given $x^2 - 6$. Compare this to the formula $x^2 - b^2$, it suggests that $b^2 = 6$.

The next step is to solve for $b$ by taking the square root of both sides:

$b^2 = 6 \Rightarrow b = \sqrt{6}$.

Thus, the missing number that completes the expression is $\sqrt{6}$.

Therefore, the solution to the problem is $\sqrt{6}$.