Question

The expression: Can you explain how to factor out the 1/3 from 2 in detail I am having trouble.

Answer 1

Answer:

Explanation:

If you multiply (x - k)(x + k), you get $x^{2} + k*x - k*x - k^{2}$ which is equal to $x^{2} -k^{2}$. Now you can see that  $\frac{1}{3} *x^{2} - 2$ must be equal to $\frac{1}{3}*(x^{2} - k^{2})$ which is equal to $\frac{1}{3}*x^{2} - \frac{1}{3}*k^{2}$. Now we just need to solve $2 = \frac{1}{3}*k^{2}$. The final answer is $k = +- \sqrt{6}$.